An internal charge pump with a cap is equivalent to an external integrator with a reference voltage equal to no phase error.
When the phase error is a pulse controlled current source going into capacitive load , they call it a charge pump or essentially an integrator. This is an essential part of the PLL to reduce steady state phase error to zero but tends to make it more unstable with delay. A series RC circuit gives proportional and integral gain improves this..
This current pump makes it easy to implement the classic PI part of a PID compensation feedback loop. Both of these give faster lock-in time with more bandwidth and reasonable jitter while having enough gain margin to remain stable. PLL tradeoffs must be chosen carefully to give desired characteristics of lock-in time and phase jitter.