Pulse counting (called photon counting when making optical measurements) is used for very low signal levels when the signal consists of discrete voltage spikes. A discriminator on the input passes only voltage spikes above a set level (signal) and rejects voltage spikes at lower voltages (noise). In this way The pulse counter counts each discrete input pulse over some time period and outputs a count rate.
For repetitive pulsed signals such as optical fluorescence, the pulse counting can be gated to occur only during a fixed time window, similar to the signal integration by a gated integrator. Similarly to a gated integrator the gate can be scanned in time to obtain the transient.