HISTORICAL:
Wooden vessels I will ignore. I am also going to ignore certain specialized vessels, such as Submarines.
Ironclads (Monitors)
The Gloire was the first Ironclad in the world; the French ship, which was the size of a WW2 light cruiser, or a modern Destroyer, was basically a wooden ship, clad in Iron. This sort of design, and designs based more heavily on Iron, became the lead "battleships" of the era between 1860 and roughly 1880-1895. Displacement normally between 5,000 tons and 15,000 tons, or, 5KT-15KT (Note that these are rough estimates as not all sources are clear as to if they are using Metric Tons, British/Long Tons, or American/Short Tons)
Pre-Dreadnought (Battleship)
Reaching its full potential in 1895, but evolving since 1880, the Pre-Dreadnought is noted as being made fully from Iron (and Steel, etc) as well as, importantly, having gun turrets that can freely rotate. A vessel of note in this class is the Mikasa, a Japanese ship that is now a museum. The final pre-dreadnoughts finished construction in 1911. Displacement of 10KT-15KT
Battleship (Dreadnoughts)
Built between 1906 and 1946, these vessels were designed to not only take on smaller ships, but destroy enemy Battleships. These became seen as the strongest ships on the sea, and the pride of the fleet. In general, when you think of a "Battleship" you think of one of these. 15KT-45KT (Yamato class far exceeds this range)
Battlecruiser
Some might say this was a failed design, and others might claim it was unclear; but these were "fast" battleships that tended to be more lightly armoured.
Capital Ships - The largest and most important ships in a navy. Historically this has been Battleships, Battlecruisers, and Aircraft Carriers, as well as the heavier Cruisers. Due to the obsolescence of Battleships, the idea of a "Capital Ship" has become depreciated.
WW2 ERA
AIRCRAFT CARRIER
The first ship to allow fixed wing aircraft to fully take off and land was the HMS Argus, which went into service in 1918. Japan and the United Kingdom were the two primary users of these early carriers with France and the United States showing an interest. The limitations of aircraft of the time meant that these ships, while very useful, were of limited use. When the Washington Naval Treaty was signed in 1922, a larger number of navies began building carriers, in large part, as conversion of ships originally designed for other purposes. The first purpose built carriers were the Hoso and Hermes, with the Bearn from France also being completed in the 1920s. The US built its first converted carrier in the 1920's as well. France would only ever have a single operational carrier while the UK, USA, and Japan all had at least a dozen.
These four nations would be the only four operating full on carriers (VS simple Seaplane tenders [Italy, Sweden, Romania], or Merchant carriers [Netherlands] which could only carry old and tiny numbers of aircraft) The main purpose of Aircraft Carriers would be to carry aircraft that could be launched from the vessel and then have said aircraft land to return them. As the war progressed, these replaced Battleships as the 'most important' ship in the fleet. An example of this class is the USS Intrepid. (7KT-38KT) [Shinano heavier]
HEAVY CRUISER
With the limits placed on Battleships by the Washington Naval Treaty, Heavy Cruiser production went into overdrive during the interwar period. By the time of the London treaty in 1930, many navies felt the current number of Heavy Cruisers in their fleet was acceptable. The role played by these ships tended to be similar to that played by Battleships, only on a smaller scale. As a result and largely for the same reasons Battleships fell out of favour with navies, Heavy Cruisers would not last much beyond the war. An example of a Heavy Cruiser is the USS Salem. (7KT-17KT)
LIGHT CRUISER
Due to the lack of limited numbers in the London Naval Treaty, many Light Cruisers were built in the lead up to the war. These ships would prove excellent in providing Anti-Aircraft fire, and cover for Carriers and other larger ships in the fleet. With Torpedo tubes and Depth Charges, these ships were extremely versatile and as the war progressed became one of the most useful types of ship. Examples include the HMS Belfast. (3KT-12KT)
DESTROYER
One of the most common ships lost in the war was the Destroyer. As the war progressed, these ships became known for submarine hunting, and somewhat useful in an anti-air role. Their smaller size and affordability meant they could be produce in high numbers and quickly. The HMCS Haida serves as an example of a Destroyer. (1KT-4KT)
FRIGATE
These ships evolved into being during the war as ships smaller than Destroyers whose main purpose was escort duty. These would see use escorting convoys. The US designed Destroyer Escort filled a similar role, as did the Kaibokan, F-boat, and other class names given to such ships by nations. An example of this type of ship is the HMAS Diamantina. (1KT-2KT)
CORVETTE
Brand new, these ships were designed for the war. The name itself comes from Winston Churchill who wanted it revived as it had previously been used for wooden naval vessels. Also known as "Patrol Gunboats" these smaller ships could be constructed at smaller shipyards around the world and were useful in hunting submarines and minesweeping. The Flower Class is likely the most well known Corvette type of its era. (1KT)
The example ship for the Corvette is the HMCS Sackville. And like the example ship from every other class used in this WW2 section, is a current "Museum Ship". Most of which, if not all, can be visited today.
MODERN ERA
AIRCRAFT CARRIER, FULL SIZE
Only two countries have "full sized" aircraft carriers, the United States, and France. These are of CATOBAR design, allowing for the use of full on jets. The US has 11 of these, all between 100KT-105KT. The single French carrier is 42KT.
AIRCRAFT CARRIER, SMALL
Unclear in exact definition, this basically includes all aircraft carriers not of full size. Generally this means STOBAR carriers, which can only handle certain jets with high levels of thrust compared to their weight. There are three of these, one each held by Russia, China, and India; and tend to be between 45-60KT in displacement. Certain STOVL carriers, which require specialized jets such as Harriers, typified by the single UK carrier (65KT), but Intia (45KT), Thailand (12KT), and Italy (27KT and 14KT) also have similar vessels.
HELICOPTER CARRIER
More numerous than either of the above, many nations have such carriers, including the US, France, Japan, Egypt, Brazil, South Korea, Spain, and Australia. Technically, since larger carriers can also handle Helicopters, Thailand, Russia, and the UK should be added to the list. (19KT-45KT)
HEAVY CRUISER
The distinction between a "heavy" and "light" cruiser no longer exists, however, it should be noted that the modern Kirov Class of cruiser would certainly fit the bill; being far heavier (25KT) than other modern cruisers.
CRUISER
The only country with Cruisers (except those outlined above) is the United States, however, some Destroyers in service are arguably large enough to be Cruisers. The most numerous vessel in this class is the Ticonderoga Class (10KT)
DESTROYER
The model of the larger modern warship. This is the typical class of ship that the larger world navies have. These ships are generally called out to action where a Frigate would not be sizable enough, or long range enough, for the job required. The Arleigh-Burke destroyer is likely the most well known of its class [in part due to its penchant for running into cargo ships] (3-10KT)
FRIGATE
The standard backbone of the modern navy. Most nations with a navy will have at least one Frigate. The US officially has none; but their coastal defence ships, the "Littoral Combat Ship" class effectively fills the same role. (2K-7K)
CORVETTE
Smaller than a Frigate, the Corvette is well used in navies that need large number of ships that can be constructed affordably; 5 of the top 6 countries with Corvettes are Russia, China, South Korea, India, and Indonesia, in that order, with the United States having over a dozen such vessels as well. The Israeli Navy, for example, has these as their largest vessel, with three Sa'ar class corvettes. (0.5K-3K)
PROPOSAL
Given the current usage patterns, and sizes of modern ships, it is my proposal that it has become time to re-classify the entire fleet of navies around the world.BATTLE CARRIER
These would be vessels that can carry full sized naval jets. The hullcode for these would change. CV was historically used, with the C standing for Cruiser, and the V for Voler; French for "to fly". CV this meant a Cruiser for Flying things. This would be reversed, and updated, with Battle Carriers now being tagged VB, for Voler and Battle. An additional letter can, and should, be attached to all hullcodes to indicate additional ship status, VBN for example would be a nuclear powered carrier. Where no "third letter" is needed, the letter for the main role; V in this case, should be repeated, for VBV.
LIGHT CARRIER
Size would not determine what these are, as above, but this would include any carrier that does not operate full sized jets; and, would include larger drones or helicopters, but mainly include any naval vessel whose main purpose is to carry jets/helicopters/drones (while excluding surface combatants who happen to also carry them) Hullcode VL; with Drone carriers as VLD, Jet carriers as VLJ, and Helicopter carriers as VLH.
BATTLE CRUISER
The Kirov class, and larger Cruisers, are clearly not simple standard "Cruisers". As such this designation would be brought back for the Kirov class, and for future larger classes as well. In general, qualification for this class would require at least 10KT of displacement, but ships with new weapon systems that are highly useful/destructive can also qualify. Hullcode BC. As the Kirov class is Nuclear powered, BCN would likely be used.
HEAVY CRUISER
With arguably more power than old Battleships, modern "Cruisers" full much of the psychological rule that Heavy Cruisers did decades ago. As such ships like the Ticonderoga Class, as well as the Chinese Type 055 "destroyer" (12KT) would be classified as Heavy Cruisers. Hullcode CA; with CAG (Guided Missile) used for the Ticonderoga.
LIGHT CRUISER
Modern "Destroyers" have strayed a great deal from their original design and intention; and fill roles that Light Cruisers once did. There is also a clear distinction between a Destroyer role and that of a Frigate; a larger gap that once existed (as some "Frigates" were thought of as "Escort Destroyers") and is better represented by the gap between Cruisers and Destroyers. Hullcode CL (CLA would be for an Anti-Air vessel)
DESTROYER
Frigates now fully fill the role once taken by old Destroyers. As a result, they will simply be re-classified as Destroyers. Hullcode DD. (DDA for Anti-Air would probably be the most common; but DDC for 'coastal' would be use for the LCS class)
FRIGATE
As noted above, the Corvette was invented in WW2 as a ship smaller than a Frigate. These ships are now larger than Frigates were at the time. The "Corvette" tag would thus be again repurposed, and Corvettes would be re-classified as Frigates. Hullcodes would start with FF, with any 'general' ship being FFX instead of FFF to avoid a triple letter usage.
CORVETTE
This definition would be allowed to drift, and, would currently be a 'catch all'. The Hullcode would be a single X with two letters being used to signify what the ship actually does, XMS for minesweeping, XAW for Amphibious Warfare (IE troop landings) XPB for a Patrol Boat, and so on. This would be the most widely disparate class in size, as some vessels (Patrol Boats) are a mere 300T (0.3KT) and others, such as the USS Lewis B. Puller, Sr. (Mobile Landing Platform) are a whopping 78KT.
SUBMARINES
I have been avoiding Submarines as their general role - going beneath the waves - has not changed, and, they've always been lumped into a class of their own, and, remain so. However a slight modification to Hullcodes is called for. SS will be replaced by S, with Nuclear powered subs becoming SN and non-nuclear powered subs remaining SS. Subs with nuclear missiles as weapons would become SNN (or SSN) while those with non-nuclear guided missiles would become SSG. Those without missiles are generally attack submarines would would be SSA.
It is important to note that due to 'class creep' and the intention of certain nations to keep their capabilities secret, that transfers would not always be 100%. As pointed out, a Chinese "Destroyer" would be re-classified as a Heavy Cruiser. There may be a small number of current Frigates that do not fit the role of the new Destroyer class, and as such, these few ships may remain Frigates, or even become Light Cruisers. This is a generalized proposal based on my observations. It is simply "for fun".