Guitar distortion pedals, particularity ones like the SD1, have EQ’s shaped to sound good on guitar and to stand out in the mix. These EQ’s often will not suit vocals, unless a special effect is desired.
Pushing a mic pre-amp a little too hard is a simple and effective way of getting good vocal distortion. Nigel’s rack pre-amps are an option, as are the pre-amps on mixing desks (as shown by Thom’s guitar on Bodysnatchers). Vocals may have been run through guitar or bass amplifiers, or subtler methods like tape saturation could have been employed. Thom could even have just sung too loudly too close to a mic.
I wouldn’t be surprised if all of these techniques were used at some point over the years. There’s no right way of getting good distortion, and what sounds good on one track might sound terrible on another. Try a bunch of things and see what you like!