We were widely using the fir filters other than IIR filters. The basic difference between IIR and FIR is if you write the system function we can observe that for the FIR filters we have only numerator but IIR filters we have both numerator and denominator. So for the IIR filters we have poles(where the system response is infinite ) where as for FIR filters we have only zeros(where system response is zero). FIR filters have linear phase response for this it has constant phase delay and group delay. That's why we are widely use FIR filters only...

Fir filter is non recursive where as iir filter is recursive

FIR involves more cofficient than IIR which may vary the Storage ,time and processing problems. Bur due to FFT chips FIR is widely used nowadays.

FIR filters are the finite IR filters and IIR are the infinite IR filters and both are used in the digital systems for the filtration purpose.