Disintegrations per second (dps), also known as decays per second, represents the number of atoms of a radioactive isotope that decay per second. One becquerel is equivalent to one disintegration per second.
Counts per second (cps) is the number of disintegrations per second, as measured by a radiation detector. This detector will not be perfect i.e. it will not detect all the decays. Therefore the counts per second is less than the disintegrations per second.