Whats is the difference between FIR/IIR filters and Chebyshev/Butterworth filters
Chebychev and Butterworth filters can be transformed with the bilinear transform into IIR filters.  The amplitude and phase responses will be warped according to the bilinear transform.  This warp mainly makes for a higher cutoff rate than the corresponding analog filter (handwavingly, it's because the antialiasing filtering and sampling already does part of the work) which tends to be ok for most applications.

In contrast, using a bilinear transform on a Bessel filter is quite pointless since its salient design feature is a near constant phase delay in the pass band, and the bilinear transform warp messes this up.  So there is a separate digital equivalent to Bessel filters that isn't related via simple bilinear transform.

FIR filters, in contrast, don't have straightforward connections to analog filter designs.  Their design procedures are quite separate and only suitable for digital filters.