Short-circuit
The current rises very sharply and can reach a very high value. Protection must operate immediately.
Overload
The current is higher than normal but not necessarily huge. The damage is caused by overheating over time.
Why we need both
A protection circuit breaker may have a thermal element for overload and a magnetic element for short-circuit.
Example
A stalled motor can create an overload, while a phase-to-phase or phase-to-neutral contact can create a short-circuit.

