Here in the UK a moulded case circuit breaker is generally understood to mean a larger and more sophisticated unit than those used for small branch circuit protection.
MCB= miniture circuit breaker, a small relatively cheap unit primarily intended for protection of subcircuits (branch circuits) or for building into equipment.
Not adjustable, has fixed and often rather crude settings.
Cant be maintained, a disposable product.
MCCB=moulded case circuit breaker, larger than the above in both dimensions and electrical ratings. Primarily intended for the protection of submains (feeders) large loads, utility scale transformers and the like.
Has adjustable trip settings, often for both thermal and magnetic trip.
Often equiped with auxillary contacts for remote indication, warning of tripping etc.
Case is moulded together, not intended to be dismantled, requires complete replacement if defective.
Self contained, no external battery required.
ACB/OCB/VCB etc. larger types of circuit breaker intended primarily for substation and utility scale applications.
Often with sophisticated adjustable features.
May be equiped with remote tripping and setting, therefore useful for remote control, not just fault protection.
Not normally self contained, usually requires an external battery for tripping.
Requires specialist maintenance.