Overdrive is a natural 'distortion' of the sound where the signal is too much for the amp and distorts. It is usally created in an amp with a preamp which boosts the signal to create an overdrive. This means an amp like a Marshall or whatever would have overdrive.

Distortion is the artificial creation of the sound like in stomp boxes and stuff. To use distortion you would usually have a pedal running into an amp on a clean setting.

Both are used for the same purpose though.