Overdrive is more soft. It's when you are pushing an amp a bit with a bit of gain but not so much as to get the sound really "distorted"... Think of blues! If you add a bit more gain, you get more "crunch" à la Eric Clapton! Yet, it's not very dirty. There is not a lot of distortion.
Distortion is what you get when you add a lot of gain, from (Hard rock - metal songs..., etc)
Overdrive pedals are (usually) not going to give you a lot of gain. You won't rely on them to play metal. You'll need more gain for that! You'll need a distortion pedal!
Or think of it like this:
Clean ---------- A bit dirty----------- A bit more dirty ----------Distortion!!
Clean ---------- A bit less clean------A bit more crunch-----------Dirty!!!
Clean-----------A bit of overdrive--------Overdrive----------------Dirty!!!
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Edit: here is a good explanation, I think:
http://www.dolphinstreet.com/blog/di...-overdrive.php