There are many types of circuit breakers(oil,air,SF6,vacuum etc) but all of them do the same functions namely making or breaking a circuit.
Generally speaking big CBs are classified as Type A or B and capabliities(Ir,Im,Icw,Ics,Icu etc)
MCCBs as general use current limiting,motor type etc
MCBs are classified as type B,C,D etc due to tripping characteristics of load(resistive,inductive,motor,fluctuating,welding etc)
Refer http://www.electrical-installation.org/lv switchgear functions and selection