Long long ago in a galaxy called the 1970's BOSS & Ibanez coined the term Overdrive. This was before the TubeScreamer and Ibanez's attempts at overdrives we're closer to what we know today as distortions as they were reportedly thin and fizzy sounding.
The overall tones are similar to the SD-1 which took over from the OD-1 in the 80's featuring asymmetrical clipping (whereas the Tubescreamer has symmetrical clipping) causing the OD-1 and SD-1 to sound smoother. The pedal was highly desirable in the 80's as it allowed players to push their amps into saturated beasts and many players still use this and variants of the OD-1 today!