What is the difference between MCB and MCCB?

MCBs or Miniature Circuit Breakers are electromechanical devices which protect an electrical circuit from an overcurrent. The overcurrent, in an electrical circuit, may result from short circuit, overload or faulty design. An MCB is a better alternative to a Fuse since it does not require replacement once an overload is detected.

MCCB or Molded Case Circuit Breakers are rated current up to 2,500 A. Thermal or thermal-magnetic operation. Trip current may be adjustable in larger ratings. Low-voltage power circuit breakers can be mounted in multi-tiers in low-voltage switchboards or switchgear cabinets.

The main difference between MCB and MCCB is the current ratings.
MCB – Used for Applications which requires less than 100A.
MCCB – Used for Applications which requires less than 1000A.

MCB is a miniature circuit breaker which is used to break small currents.  Like in domestic LT circuits. The ratings usually end up to 100 A.

MCCB is a Module case circuit breaker which has a rugged construction as it can break larger currents usually from (100-1000A).

The breaker mechanism is more or less similar in both of these either magnetic or thermo-magnetic.
Usually MCCB of higher range come with adjustable short circuit assembly with a relay and motor for spring for remote operation just like ACB but without arc runners and chutes.