What kind of ship capability, specifically, gives the STAR designation? What about BATTLE? BAY? What can I make up that makes these things make sense?
On Earth, mid-20th century, BATTLE refers to a size of gun. If a ship has guns over a certain size, then it's a battleship or a battle cruiser. Since BATTLE refers to weapons, what weapons must a battlestar carry that grants them the BATTLE status?
Nuclear weapons seems to be the easiest choice, but we know that Cylon fighter carry nuclear weapons, so that indicates that intermediate sized ships can carry nuclear weapons as well. Nuclear, by itself, is not a useful metric. Missile size? I don't know how to define that. Megatonnage of deployed missiles? Again, a small ship can carry a single large-tonnage warhead. Following this logic clarifies nothing.
Does BATTLE refer to fighters? If so, then the Cylon ships should have the BATTLE designation as well. As they don't, there must be a different between the armaments of a battlestar and a baystar. BAY must refer to something, but I don't know what.
STAR is equally frustrating. Does STAR refer to a size of ship? That seems most likely. The largest ships get the STAR designation. A STAR could refer to a carrier. We see a number of battlestars over the course of the show, and they all are carriers, some larger than others. If there is such a size discrepancy, then STARS can't just be the largest ships. Of course, one wonders why they aren't called carriers, but Battlecarrier Galactica just doesn't have the same ring to it.
As for FTL being a criteria, every military ship that we see (except vipers) has a jump drive. They're not all called STARs, so FTL can't be a criteria.
So, what should I, as a writer, want to do with that mess above? The answer, of course, is to make shit up, because that's what I like doing.
BATTLE refers to any capital ship of the Colonial fleet. Because of strategic and tactical requirements, all Colonial capital ships of this time period act as carriers, so BATTLE refers to a combined array of heavy conventional weapons, one or more flight groups, significant anti-aircraft weapons, and significant armor. STAR is an abbreviation of STARSHIP, a distinction useful when Colonial militaries still maintained terrestrial war fleets, but has lost its utility by the time of the show. Battlestars use their fighter groups to punch holes in Cylon defenses, then the battlestars move in to duke it out the the baystars up close.
BAY refers to the storage bay of Cyclon fighters. Because Cylon fighters are Cylons, they act as both crew and ship, so their storage arrangement gets its own definition. Each fighter is bayed on the STAR, thus, you have a baystar. As baystars rely on swarm fighter tactics and boarding actions to destroy battlestars, they carry significantly lighter conventional weapons, far fewer anti-aircraft guns, and less armor. A baystar's preferred tactic is to stand off from the main battle, jumping its fighters in.
In a stand-off confrontation, a baystar usually has the upper hand on a battlestar, using its superior numbers to grind the humans into exhaustion. Battlestars prefer closing with the enemy, using their heavier conventional weapons to disable the lighter baystars.