The terms "distortion", "overdrive" and "fuzz" are often used interchangeably, but they have subtle differences in meaning. Overdrive effects are the mildest of the three, producing "warm" overtones at quieter volumes and harsher distortion as gain is increased. A "distortion" effect produces approximately the same amount of distortion at any volume, and its sound alterations are much more pronounced and intense. A fuzzbox (or "fuzz box”) alters an audio signal until it is nearly a square wave and adds complex overtones by way of a frequency multiplier.
So How do I know which is best for me?
Generally speaking Overdrives offer more subtle differences than distortion or fuzz. If you primarily want that creamy overdriven sound of a tube amp when it is just breaking up then look to an overdrive. For those of us lucky enough to have those old powerful tube amps like say; a fender twin but have to play at low volumes, an overdrive is awesome because it can simulate how the amp would act at higher volumes. On the other hand if you are a fan of classic rock or more hard edge genres a distortion pedal will be more suited. If you want to replicate the sounds of some of the late sixties, early seventies music “Think revolution by the Beatles”, a fuzz will sometimes be the answer. If you are covering many styles of music, you may want all three. For more in depth information we found these helpful post.