All three catalytic triads in trypsin, chymotrypsin, and elastase are identical, with similar overall structures. The varied amino acid residues around the catalytic site are able to change the binding of substrate, giving each protease its specificity.
The three proteases were likely formed through divergent evolution, with the enzymatically important residues and domains being conserved while the selectivity residues changing to allow different substrates to be cleaved.
The triad is only involved in the cleavage of the scissile bond – it does not convey any specificity for a certain substrate. The selectivity pockets are formed by the residues surrounding the catalytic triad, allowing the proteases to cleave specific sites.