Technically, I think "servo" refers to the presence of a position feedback mechanism, rather than a particular type of motor. MOST servos of the sort used in hobbyist radio control things use ordinary DC motors (thus the "simplicity" of conversions to continuous rotation), but some proudly proclaim their use of "coreless" motors. Large industrial servo motors are likely to have custom-manufactured motors carefully tuned to the needs at hand (an awful lot of industrial motors seem to be near-custom, whether used in servos or otherwise.) It would be possible (and an interesting exercise) to make a servo using a stepper motor. Microservos use motors that look very much like pager motors.
Usually the hard part of a servo is the gear-train. the electronics is conceptually simple, and the motor choice is flexible. (and there have been some interesting results in micro-realm by getting creative with the gears and mechanical construction.)