From what I recall:
-MCB is a main circuit breaker, which can be any type of 
circuit breaker
-MCCB is a Metal Clad Circuit Breaker, which is generally 
rackable from its slot and typically used for breaking much 
larger loads.

mcb in nothing but miniature circuit breaker it is 
generally used for low current rating whereas MCCB is 
moulded case circuit breaker this is used for high ampere 
(load)rating

MCB is used where ever there is an balanced current flow in 
three phase, it will maloperate in unbalanced load condition

But MCCB is used in place of high rating current and also 
in place where there is unbalances in current it will 
operate correctly in this condition

MCB is a miniature circuit breaker that can safely break 
only a small amount of short circuit current. The O/L and 
S/C protection releases are factory calibrated and is not 
adjustable at installation points. Max. available in India 
is 10 KA. This its application is at the lowest end of 
power utilisation such as small power, lighting and for 
some small motor applications.

MCCB is a moulded case circuit breaker capable of switching 
on and off a large amount of power. It is designed to carry 
large amount of making current and breaking current. It 
comes with -accessories like hunt trip, UV release, 
adjustable short circuit and overload protection releases, 
earth fault release etc.

MCB is not having the adjustment of protections like Over 
Load, Short circuit, Earth fault and Instantaneous current, 
but MCCB is having.