Aren't both the same thing? Why then use different terminology?
AC generators can be broadly referred to any type of electricity generator that generates electrical energy in Alternating Current (AC) form. So, in a way, yes, an Alternator is also an AC generator.
A more appropriate term for an alternator is - AC synchronous generators.
More specifically, in an alternator, the excitation winding (which produces magnetic field) is mounted on the Rotor shaft and the armature winding (which generates electrical current) is mounted on the Stator (stationary part of machine which surrounds the rotor). While in most of the other types of electrical generators, including DC generators, the excitation winding is stationary and the armature winding is mounted on the rotor shaft.
So basically, you may distinguish it like - the magnetic field is stationary in generators, while it is rotating in alternators. Or the other way - the armature winding is rotating in generators, while it is stationary in alternators.
Take it like this, all alternators are AC generators but NOT all AC generators can be alternators.