MCBs are available with different tripping characteristics.
They are available in types 'B', 'C' and 'D'
They all have the same characteristics for disconnecting overload currents. This is where you draw a load larger that the rating of the MCB for a period of time. It warms the thermal part of the MCB which causes it to trip.
They have different characteristics for dealing with fault currents. This is where a very large current flows in a circuit, normally due to a short circuit. This operates the magnetic part of the MCB and causes it to trip.
These are available with different sensitivities. It will take a larger fault to trip a type 'C' MCB than it will to trip a type 'B'.
This is useful for appliances with medium start up currents such as motors and banks of fluorescent lighting, but as the magnetic part of the MCB is less sensitive, you need to ensure the earth to the circuit is good enough.
If the earth has a resistance which is too high, then in the event of a fault to earth, the circuit will not disconnect quick enough, so it is very important to verify this before replacing the MCB.
You can also get type 'D' MCBs, but these are normally only used for specialist installations with very high starting currents such as large welding sets, x-ray machines and some theatrical dimmers.
Hope that makes sense. I've tried to keep it in laymans terms.