In a way, they are both the same. They are both shorts technically, but with important differences.
A short is two normally current carrying conductors make contact unintentionally in a way that bypass the load. For example, L1 touches the Neutral. In this case Amperage will rise until the OCPD trips
A Ground Fault is when normally current carry conductors make contact with non-normally current carrying conductors or surfaces. For example, L1 touches a metal enclosure.
Assuming the ground-fault is to a properly grounded surface, again amperage will increase until the OCPD trips.
If the GF is to a conductive surface that is NOT properly grounded, there is no path for current to flow, so the breaker will not trip. This is dangerous because you now have a live surface (same as the bare wire), waiting for somebody to complete the circuit through their body.
GFCI's sense current flowing to ground to help detect and break a ground faulted circuit
Arc faults are yet a differnt scenario