Why are slip rings used in an AC generator but not in a DC generator?

Slip rings provide a means for connecting the rotating armature of a simple a.c. generator to an external circuit. As the armature naturally produces an alternating voltage, an alternating voltages is what appears across the slip rings.

To obtain a d.c. voltage, it's necessary to reverse the direction of the natural alternating voltage every half cycle, producing full wave rectification. This is achieved using a split-ring commutator which, essentially, is a rotating switch.

So, slip rings are used with simple a.c. generators, whereas a commutator is used with d.c. generators.

Having said that, however, large modern a.c. generators (alternators) have fixed armatures, and rotating fields, and slip rings are used to supply d.c. field current to the alternator's rotating field windings.