Well obviously BFG ship abbreviations derive from their real world counterparts originally but have been co-opted to make sense according to the classes and types available in BFG. This system is pretty simple (maybe even simplistic), in that the first letter is the hull type and the second letter is the role. If the second letter is the same as the first then it just means that its role is typical of its type. The only exception being the CA (basic attack cruiser) which is not CC because of the possibility at some stage of introducing Corvette sized craft.
So a CB would be a "Cruiser, battle" and CV is a "Cruiser, carrier" and CL is "Cruiser, light". Sometimes there's 3 letters, such as CVL "Cruiser, carrier, light". Chaos Heavy Cruisers are as similar to IN CBs as Chaos cruisers are to IN cruisers, hence both are classified as CB (rather than, say, CH for a heavy cruiser).
As for a battleship sized carrier, that would be emended as BV (Emperor, Despoiler, Nemesis, Explorer), whereas Horizon has it as CVB, which would really be a battlecruiser level carrier (as exemplified by the Jovian and Styx and to a lesser degree the Mars). CG is, of course, "Cruiser, grand" for which there is no real world analogue except for perhaps a true battlecruiser, and CVG would be a "Cruiser, carrier, grand" which is basically a Retaliator or Exorcist.