FreeSpace ship size designations work just as real life does, with the exception of cruisers, which have been moved below corvettes into the space filled by 'gunboats' or cutters or the like in reality.
From smallest to largest it runs
cruiser - basically for very light patrols and minimal combat in support of fighters
corvette - the smallest 'line warship' in freespace, capable of holding its own against fighter and bomber squadrons and attacking corvettes in groups
frigate - a larger, more powerful corvette, often retaining great speed and flexibility
destroyer - the first capital ship class, the centerpiece of a battlegroup, with both powerful main guns and the ability to carry and launch fighters
(superdestroyer, which is more a destroyer with fancy stuff than a bigger destroyer)
carrier (a destroyer with fewer guns but more ability to carry fighters)
dreadnought (historically a big ship with a set of very large guns of the same calibre)
juggernaught (something big and hard to stop)
For fighters:
Space superiority - tough, all-around combatant designed to shoot down other fighters and prevent them from causing trouble
Heavy assault - a fighter craft still capable of dogfighting but also loaded with a lot of ordnance for attacking light targets like cruisers and freighters
Light bomber - bomber that carries mostly anti-turret/subsystem weapons
Strike bomber - fast bomber design capable of carrying heavy warheads
Heavy bomber - big slow bomber, needs to travel with escort, carries large amounts of the heaviest warheads