Different types of circuit breaker, including the common B, C, D types and the more unlikely K and Z.
Circuit breakers contain two elements - a thermal part which reacts to moderate overloads, and a magnetic part which reacts to short circuits. The thermal part is the same in all types and takes a moderately long time to disconnect - seconds to several minutes.
The magnetic part is designed to trip near-instantaneously, and the current at which it trips depends on the type.
Trips between 3x and 5x the rated current. Example - a 6A circuit breaker would need between 18A and 30A before it trips.
Trips between 5x and 10x the rated current. Example - a 20A circuit breaker would need between 100A and 500A before it trips.
Trips between 10x and 20x the rated current. Example - a 16A circuit breaker would need between 160A and 320A before it trips.
Less common, this type trips between 10x and 14x the rated current. This is within the trip range of the D type.
Another uncommon option, type Z trips between 2x and 3x rated current. This puts it below the trip range of the type B.
All types trip at much higher currents - the range is the minimum required to trip the device.
This document from ABB covers the various types in more detail.
Devices with higher trip currents are used where the load has a significant inrush current when starting - devices such as motors or lighting with magnetic ballast units. Use of devices with a lower trip current could result in tripping when a device is first switched on.
However it is not appropriate to simply change to a type with a higher trip current to avoid unwanted tripping - the impedance of the circuit must be checked first to ensure that in the event of a fault, the MCB will disconnect within the required time.