Overdrive is actually clean sound, which is 'overdriven', set to high gain at high volume, thus the name 'overdrive', and its 'broken, heavy characteristics'.
Distortion, is rather cutting, enhancing and distorting of the sound itself, at an extreme level, thus, the heavy, distorted sound...
Yupz, like what mikemann said, Ds-1 is a good pedal for modding and stuff. There are tonnes of distortion pedals out there really, like the sansamp, the proco rat series, tubescreamers(TS-XXX) from Ibanez, Visual Sound's route 66 and jekyll hyde, and even Boss has a few to begin with.
Each has different characteristics, and something that's good for one, may not be another's. Thus, it is best if you try it yourself, and see whether it suits your type of music, and your wallet of course! =)
Well, there's also fuzz, which is a kind of distortion, unique in its own self, and quite interesting really...and yeah, i love the jekyll & hyde from Visual sound, but it takes a lot of patience to learn to love this dude...coz if you want to get the best out of both channels, you really gotta tweak it..
At the end of the day, it really comes down to your own personal choice. Some choose to invest in better pickups, for higher outputs/better tonal characteristics, while others spend their time GAS-ing.. and some lucky ones gets both!