For many applications, the FIR and digital filter (IIR) can be used interchangeably. However, they do have a few key differences:
1) FIR filters have a linear phase response. They create minimal signal distortions in the time domain.
2) IIR filters are computationally inexpensive compared to FIR filters. The propagation delay is typically shorter.
3) FIR filters can easily create very steep cut-off corners, where the slopes of IIR filters are less tunable.
4) IIR filters have analog counterparts. You can use the IIR filter to simulate analog filters or the other way around. FIR filter can only be implemented digitally.