Bacterial CRISPR systems provide acquired immunity against invading nucleic acids by activating RNA-programmable RNases and DNases. Cas13a and Cas12a enzymes bound to CRISPR RNA (crRNA) recognize specific nucleic acid targets, initiating cleavage of the targets as well as non-target (trans) nucleic acids. Here, we examine the kinetics of single-turnover target and multi-turnover trans-nuclease activities of both enzymes. High-turnover, non-specific Cas13a trans-RNase activity is coupled to rapid binding of target RNA. By contrast, low-turnover Cas12a trans-nuclease activity is coupled to relatively slow cleavage of target DNA, selective for DNA over RNA, indifferent to base identity, and preferential for single-stranded substrates. Combining multiple crRNA increases detection sensitivity of targets, an approach we use to quantify pathogen DNA in samples from patients suspected of Buruli ulcer disease. Results reveal that these enzymes are kinetically adapted to play distinct roles in bacterial adaptive immunity and show how kinetic analysis can be applied to CRISPR-based diagnostics.