the magnetic trip is different, but the thermal trip is the same
Type B trips at between 3-5 labeled rating instantly, for type C its between 5 and 10, and for type D between 10 and 20.
You have to make sure the ELFI is low enough for the breaker you use, the elfi dictates the size of the current that will flow in a phase-earth fault and this must be sufficent to trip the breaker instantly, the reason you don't use type Bs all the time is because some equipment (things like motors and loads incorporating capacitors) takes a surge on start up and this can trip breakers even though there isn't a fault.
Generally speaking, Type B is general purpose, Type C is used where there are motors, and sometimes on circuits supplying lighting and power supply cicruits. Type D are rarely used and are for things like welding machines, X ray machines, etc