In RC modeling parlance, an "analog" servo uses an older technology analog servo amplifier (amplifier = controller in this terminology). A "digital" servo uses a servo amplifier with a microprocessor in it. Digital servos tend to have more torque and highershorter response times for the same motor and mechanical assembly.
(Note that there's no fundamental reason you couldn't build a super-hot analog controller; it was just never done, and would have been much harder to stuff inside an RC servo case, so the world had to wait for itty bitty microprocessors).