Yes, it's like Rid said... with Overdrive, it'll sound more like the basic tone, but with some overdriven frequencies, while Distortion is an unatural sound and usually sounds meaner :headbang:
At its most basic, Distortion is just lots and lots of overdrive, but there is a difference in sound - for a really distorted sound, many ppl will use pedals, whilst for a tube-like overdriven sound, lots of people stick with their amp.
Overdrive adds more power from the guitar to the amp, causing the amp to clip and causes a more distorted sound (from the amp itself). Distortion adds it's own clipping from the pedal before it gets to the amp.
I would say use a distortion pedal with a cheaper SS amp that you want to color the sound (to that of the distortion pedal of your choice), and the overdrive to push a tube amp into clipping earlier to get a more natural distorted sound from the guitar and amp.
Overdrive is a sinus with both a clean and a clipped signal as Robert said.
A distortion chops up the whole of the signal, both sides of the sinus is clipped, in various forms depending on how you filter it.