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Some of the battleships currently available in Europe and all over the world are:
Torpedo-boat These ships have been misrepresented in Empire. They were designed to kill large ships by swarming them and launching torpedoes. In fact, they were projected to be so effective that the French 'Jeune Ecole' (Young School) of naval officers advocated abandoning battleships entirely, saying that they
would be helpless in the face of the torpedo-boat. In reality, the torpedo boat was limited by it's short range, deficient sea-keeping ability, and the battleship's quick acquisition of numerous light quick-firing guns and machine guns. They were effective when used in large numbers, but tended to die a lot.

Destroyer These include three kinds of ships. First is the 1880-1910 destroyers, originally 'torpedo-boat destroyers', and meant to be cheap ships to screen the battleships. Second is the
1910-1950 version, meant to kill submarines with sonar and depth-charges. Lastly is the 1950-1965 destroyer, an all around ship, with ASW and ASuW (anti-surface armament). After that, they type mostly died out, as it had gotten too large.

Frigate Originally, these were ships of about 200-400t, with a crew of 200-500, armed with from 30-50 large cannon plus numerous small cannon. They were intended to scout for ships of the line, and protect/destroy commerce. After about 1860, the type died out entirely, and was replaced by light cruisers. In the
1960's, the type was resurrected for a new class of ASW (anti submarine warfare) ships of small-medium size.

Light cruiser The class came into existence in the 1860-1905 period to provide fast ships suitable for extended deployment in far-away places.
They were intended to out-class local defense boats, and not much else. Much was sacrificed to give them long-term speed end endurance. They were not intended to have a role in a major battle.

Heavy cruiser This class has a dual role. It was intended to reinforce the light cruisers in the colonies, providing a heavier punch and more armor, and also to be scouting elements in major fleet battles.

Ship-of-the-line pre-dreadnought dreadnought battleship While the names change, the purpose remained the same: a ship that brings heavy guns close to the enemy and destroys him. It also was much used for off-shore bombardment, and for ships of the line, minor invasions. (A complement of 300-400 marines and 600 sailors allowed a ship of the line to land up to 750 fighting men at any desired point. Small squadrons of these ships could (and did) take over towns, attack fortresses by surprise, and generally make life miserable for the defense).

The pre-dreadnought was a battleship with a limited number
(usually 4) of heavy guns, numerous lighter guns ('secondary' and 'tertiary' armament), and heavy armor on vital portions of the ship. They were hard to kill, even for themselves, as they had only a few guns that could penetrate the armor of their peers.

The dreadnought was introduced in an article in Jane's Fighting
Ships by an Italian designer, who received permission to publish his design after the Italian government decided that it was too large and expensive for them. The design/concept was seized upon by First Sea Lord Jacky Fisher, who rushed completion of the first ship, the Dreadnought, through in only 1 year. (An amazing feat and a major record) The Dreadnought gave its name to the entire type of ship, having 8-12 large calibre guns, few secondary & tertiary weapons, and good armor. (As can be guessed, the threat posed by torpedo boats had diminished considerably, mostly with the quiet abandonment of the policy of close blockade, and the advent of the destroyer)

The battleship of the 1918-1945 period was faster, and carried a new AA capacity, especially in the latter years of the period.

After 1945, the class died out (except for 4 ships)

For our purposes, a battleship 1 is a ship of the line, a battleship 2 is a pre-dreadnought, a battleship 3 is a dreadnought, and a battleship 4 is what was called a battleship or (sometimes) super-dreadnought.

Battlecruiser These special ships existed in the 1905-1920 period, prior to the widespread introduction of oil fuel. They had full battle ship guns, and a large speed advantage over the battleships, but very little armor. They were initially the pet project of
First Sea Lord Jacky Fisher, who intended them to both kill the heavy/armored cruisers of the time, and to scout for the battleships. With their heavy armament (and name), their function inevitably blurred, and they were used in combat against full-fledged battleships, where they died like flies.
With this (and with the introduction of oil fuel, which made battleships their equal in speed), they were phased out.

ASW Cruiser These ships came into being in the 1965-present period in response to a need for a large ASW ship to carry ASW helicopters and command equipment. It typically carries full ASW armament, as well as a minor ASuW capability.

Missile boat
Missile frigate
Missile cruiser These ships range in size from 100t missile boats (the modern replacement for the torpedo-boat) to the 6000-8000t missile cruiser. They all are designed to bring missiles to bear on the enemy. (The first successful missile boats were Egyptian, and used against the Israelis in the 1967 Arab-Israeli war)

The missile frigate and cruiser also serve as SAM ships.

Landing craft These ships are relatively unique, being used mainly in the
1942-1950 period. Before that, landings were carried out by frigates, ships-of-the-line, light & heavy cruisers, & pre-dreadnoughts, all of which could land a large number of men. With the introduction of the concept of beach-defense by the Germans, these ships were invented to get large numbers of men on the beaches quickly. After 1950, their functions were largely assumed by the helicopter.

Aircraft carrier light carrier escort carrier These ships are designed for various purposes. At first, carriers concentrated on scouting for the battleships. Later, it was proved that airplanes could sink battleships (Thanks to
Billy Mitchell here), and the emphasis moved to all-around sea control. Still later, with the disappearance of the battleship, a large power-projection capacity was added.

Light carriers were simply smaller versions of the large or
'fleet' carriers, and were used for the same duties.

Escort carriers were usually hastily converted merchantmen, and carried small numbers of fighters and ASW planes. (Some merchantment, in fact, were equipped with 1 fighter and a temporary catapult. When threatened by enemy planes, the fighter took off. When it was done, it ditched, and the pilot
was (theoretically) picked up by the merchant ship's convoy.
This was used several times, and worked!)

Submarine The submarine was originally intended, in the 1900-1910 period, to fill the same role as the torpedo boat, using stealth to get to the battleships instead of speed. It was a strictly defensive weapon, without much speed or endurance.

In the 1910-1925 period, the sub was much enlarged, and use in a combination anti-battleship (sank at least 20)/anti-commerce role. Endurance was much improved, and the sub could now operate a long distance from its home port.

In the 1925-1945 period, the sub steadily grew large and more capable, gaining mostly in speed, sonar ability, and endurance.

After 1945, nuclear power vastly increased the subs endurance, making it effectively infinite. Sonar was also vastly improved, and removed the reliance upon the periscope. The subs armament
was also vastly improved with the addition of the SLM & SLBM.

Minesweeper Usually converted fishing vessels, small, and expendable. They found and destroyed mines with a variety of tricks, including cables & magnetism.