Mentioned Colonial Warship TYPES
Warstar (Basically a battleship all guns no Vipers) they were being phased out and very few were remaining. Example Anteros.
Battlestars/Carriers/"Other"
Vindicator class Battlestar (only one made as others were delayed) KIA
Mercury Class Battlestar (example Pegasus)
Jupiter Class Battlestar (example Galactica)
Valkyrie Class Battlestar (example Valkyrie and Kestrel)
Atlas Class Carrier KIA
Osiris Class AKA Pocket Battlestar. The Stealthstar variant would be Osiris III but was not on official registries. Example Apis.
SDF Battlestars
Minerva (example Hades and Sulis)
Artemis (example Resolute)
The Minerva and Artemis are comparable with the main difference is the Minerva has less armor that was replaced by more weaponry. This makes the Minerva a "glass cannon."
Adamant at the time of attack only Picon had any on active duty.
Missilestars
Janus Class Gemenon SDF Flagship Janus was the last operational ship of this design. KIA,
Ranger 8 "Revolver" type missile launchers. One of the most common in ship numbers.
Rover Class 6 "Revolver" type missile launchers. The main difference between Ranger and Rover is the Ranger not only has 2 more launchers but almost twice the missile capacity. Rovers are also "shorter legged". These were done as cost saving measures for the SDFs. Example Orion.
Gunstars
Minotaur all guns no missiles example Shaitan
Escortstar example Aphid
Aegis Class Escortstar (only 8 made) pretty much only defensive weaponry was to be paired with larger ships. Example Heim.
Patrolstar the main (possibly only) ship used by the Colonial Guard (Space Coast Guard). More designed for antipiracy than combat. Example Vigilant.
Faststars
Bezerk Class (example Perseus) Bezerks are a multipurpose design. A mixture of Battlestar and Missilestar. Considered to be expensive as having higher crew needs and were also lacking in armor. Now reaching (or past) their original design lifespan.
Centaur Class (example Chiron). The Centaur were supposed to be the smaller less expensive version of the Bezerk. This did not work out that well. Individually the Centaurs are "passable" but were not successful as a general design as their basic concept was changed more than once.
Manticore (example Lamia). The Manticore is mainly a Missilestar mixed with a Gunstar. They are small and fast. The Manticores were another ship that was planned to have a completely new design made in the future as they were also reaching the end of their original lifespan for the design.
These are the military support ships with
Hospitalstar (a few were in active reserve) all KIA.
Marinestar (troop carrier with a large shuttle bay and for its size heavy point defense but very low offensive weaponry) example Priam.
Repairstar repair ship for larger jobs. Can fix on site battle damage and has extensive manufacturing capabilities. (Some were in active reserve). Example Sarek (however this was no longer "active" aka had its armor and weapon points removed).
Supplystar (similar to the Marinestar) large shuttle bay but with some (but not much) heavy weaponry example Azeban.
Other Military Ships
Missile Colliers were designed to carry and quickly resupply munitions to the Colonial Forces. Example Aglaea.
Tyleum refuelers. These were able to mine and refine enough tyleum to keep a small flotilla active. Example Minos.
Celestra Class repair ships (more helpful with long term maintenance than fixing battle damage). Example Thalia.
The Battlestar category is pretty broad. If it launches and lands Vipers (as its main job) it's a Battlestar. The Osiris (it was Orion Class in Blood and Chrome but I forgot that and kind of screwed up my other story so "meh") probably is not really a Battlestar as not only is it small it lacks much in the way of armor and weaponry. The Atlas is slow and should not be in a fight by itself but can launch a LOT of Vipers. Naval ship classes are never an exact science and for this story I will just say that you had 12 different governments that had to come up with a common terminology in the middle of the biggest war they had ever fought so sloppiness was not shocking.
The Escortstars and Patrolstar are based on the same general hull design. The Patrolstar being used for policing has better sensors with less weaponry and armor. The Aegis class was a new variant that was to be paired with some of the various "glass cannons" to increase their survivability in case of a major war and was being considered as a replacement for the most common variant of the Patrolstar design. After 40 years of the Cylon's isolationism whether Escortstars needed to be able to fight against a potential pier enemy that seems to have disappeared was being questioned.
Faststars are a mess as a ship classification. They were the cruisers of space but pretty much the "throw what is left over" category. They are generally fast at least and smaller than the Missilestars.
The differences between the various (and horribly named) support "Stars" and the other military support ships are size and basic design. Hospital, Repair, Supply, and Marine "Stars" are designed from the hull up with the idea that combat can happen and that Toasters will shoot fast moving projectiles or nukes at you. You wouldn't want to be in a Supplystar in combat but it's a lot better than being on a missile collier in the same situation.
The other support ships are modified civilian designs. They lack the compartmentalization of the "Stars" but are cheaper.
A general word. There probably were other designs or classifications but well they are dead so they don't matter.
The Colonial Forces were a bit "Carrier Heavy" (the show is Battlestar Galactica after all) but fairly balanced. There were a lot of ships in "Active Reserve" grouped in "safe spots" but the Cylons destroyed all of them. Also some of the ship designs (example the Chiron) were "proof of concept" and if a major war with the Cylons ever happened the Colonials planned on mass producing them. This of course did not work out at all the way the Colonials planned.
The SDFs were a combination of reserve, training, and costly planetary dick waving for pride as anything else. One thing in my stories is that while the Cylons were the main threat there was a belief/fear that the 12 Colonies were about 50 to 100 years from a possible civil war. The "Territories" (colonies outside the Cyrannus system) would eventually reach enough population to not want to be some natural resource exporter and worse would expect to have actual representation in the Quorum or even say "we are going our own way." OR some of the Twelve Colonies might find the Colonial Government oppressive so kept their own SDF forces so to have a core units in case of this theoretical civil war.