Bob Engelhardt writes:

Is a servo motor simply a DC motor with an encoder or tach?

That's what is often meant but even that is too restrictive. Any bare
motor with feedback and control over position or velocity would be "servo",
regardless of whether the sensing device is part of the motor. For
example, a CNC drive motor without an encoder is servo operated when the
controls read the DRO table encoders instead of an encoder on the motor
shaft.

The motor principle itself (PMDC, brushless AC, etc) is not a servo
characteristic. Low-inertia motor designs are sometimes thought of as more
properly servo types, but this has more to do with the application
requiring rapid acceleration than with the servo principle itself. There
are servo applications where you want to avoid acceleration and thus the
motor is designed for high inertia.