Battleship: very large, heavily armed and armoured. Principal fleet capital ship up until about 1943. Very powerful against other warships, but vulnerable to bomb/torpedo attack from multiple attack craft. Basically a FS destroyer like a Hecate. Shouldn't really have a fighterbay, but that would cause problems...
A battlecruiser is like a battleship, but faster and more lightly armoured. E.g. HMS Hood: Biggest ship in the world until the yanks built the Iowas, 15-inch guns, very fast, light armour. So it'd be like a Hecate with ~30% less hitpoints and 25 speed.
Monitors were heavy support vessels. Example: the HMS Roberts was about 100m long, could do about 15kts, and had a pair of 15-inch battleship guns. Was used for bombarding shore targets at the Normandy landings. I suppose the FS equivalent would be to arm an Aeolus with a BGreen beam and not much else.