Fuses and circuit breakers protect against both overload and short circuit.
These are two different things, that is why in a circuit breaker the tripping time as a function of the current is made out of
two curves.
The overload protection trips by bimetallic strips that bend when they get heated up. The heating/bending mimics the heating up of the connected cable or motor. The bimetallic strips dont trip instantanously when the current exceeds the set value, instead it is a gradual function, higher current makes the time shorter.
The short circuit protection trips basically a relay coil. So it acts in principle instantanously when the current exceeds the set value.
Here is an example of a circuit breaker tripping curve.
Notice that it is two different curves because it is two different functions.
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A fuse, i.e. a melting wire of usually silver, has a melting time that is a simple exponential-like function of the current. It can also protect against both overload and short circuit but the curve is simpler.
Both circuit breakers and fuses can be used to reduce the short circuit current, which is useful for reducing the short circuit current of an installation of a control panel. That is an entirely different and important topic.