Rocketpunk Manifesto looked at this question in a multi part series of threads about Space War (http://www.rocketpunk-manifesto.com/search?q=space+war), and the results were not quite what you would expect.
First off, space warcraft are defined by their roles much the way wet navy ships are, but since the roles of spacecraft are different , so are the names. Formations are also different, so there is quite a bit to cover.
First off, because ships are constrained by orbital mechanics, their paths are fairly predictable. IF you are doing a burn to a transfer orbit to Uranus, then there is no "sneaking away" to reach Mars unobserved, you need to apply a lot of energy to get to different transfer orbits. This is true even using Terrawatt powered Torch Drives (although in this case, you are already radiating enough energy to be clearly visible out to Alpha Centauri).
So ships will travel in mutually supporting formations known as "Constellations".
Within the constellation are ships carrying massive laser weapons, the most powerful the polity can afford to build and field, since long range laser engagements work in the favour of whoever has the greatest range. For practical reasons, this means building lasers which can vaporize metals and ceramics out to the range of one light second (almost the distance to the Moon from Earth), since beyond a light second there is a significant lag between when a signal arrives at your ship, and when you point and fire the laser. The enemy ship can apply some random thrust and ruin your fire control solution. The laser weapon is colloquially known as a Ravening Beam of Death (RBoD) and the carrying ship is a Laserstar. To make targeting the Laserstar's optical train more difficult (an "eyeball frying contest"), secondary Fighting Mirrors might be deployed remotely to make tracing the possible optical paths more difficult.
Supporting the Laserstar is a fire support ship which carries thousands of small kinetic energy projectiles. Swarms of these projectiles can eventually overwhelm even a massive Laserstar, but we are talking about thousands to tens of thousands of projectiles filling the sky. Such ships can use railguns, coil guns or simple batteries of rockets to launch the small projectiles, colloquially known as "Soda Cans of Death" (SCoD). The secondary purpose of these devices is to fill the sky with swarms of sensors to provide a fine grained 3 dimensional view of the battlespace. These ships are known as Kineticstars
Laserstars and Kineticstars are mostly unlovely assemblies of girders, power plants, fuel tankage and radiators, and rely on powerful AI's to ensure their weapons are employed to the best effect. However, these weapons are far too powerful to be allowed to go off on their own, and are massive overkill for many of the lesser missions that a Space Navy might be assigned. A manned Command and Control ship is needed for the constellation, to provide the human staff which gives the final authority for fire/not fire to the AI's.
Since some missions actually require boarding parties to inspect ships, the constellation will also need Cutters to bring inspection teams to and from the formation. Armed and armoured cutters might be included as Boarding Craft for the Space Marines, and the Admiral will also have a Lighter to travel on diplomatic or courtesy visits, leaving the constellation in high orbit to "show the flag".
Various miscellaneous Support Ships will be included in any constellation, to provide berthing space for the smaller craft, repairs for systems while under weigh and recreational space for the crews outside of their fighting craft. For practical reasons the fighting craft will be very small to reduce their signatures during the fight, and they will disperse among the ships and sensors of the deployed constellation in order to maximize their survival.
A fully deployed constellation will be incredibly impressive. There will be a swarm of sensor drones and subsidiary gunships (smaller laser and kineticstars to provide close in defense) spread out over a light second in diameter, with the massive Laserstars and Kineticstars deployed inside this disc. The Command and Control craft will also be somewhere inside the disc, to provide oversight to the deployed weapons systems, while the support ships will drop behind.