Overdrive is a type of distortion.....
I found this website that goes into detail....

http://users.chariot.net.au/~gmarts/ampovdrv.htm

I always considered Overdrive to be a natural distortion that comes from "overdriving" the tubes and Distortion as a "digital" form of overdrive.

Overdrive uses soft clipping.

Distortion uses hard clipping

Soft Clipping: This is usually marketed as "overdrive", where the gain is inversely proportional to the input signal level. This is typically produced either with back to back silicon signal diodes in the negative feedback path of an op-amp, or with germanium diodes or LEDs back to back in a shunt to ground.

Hard Clipping: Usually marketed as "distortion", where the signal level is restricted within a range. This is typically produced with silicon diodes back to back in a shunt to ground. This is the same as the circuit above, using silicon instead of germanium/LED diodes.