20, 40, what's the difference?
The .32 Winchester Special amounts to the .32-40 barrel specs and the .30-30 bottleneck chamber. No relation to the .32-20.
The part about factory loads with smokeless and reload with black is, if an urban legend, a very well entrenched one. I have an article where the writer tried it. He was disappointed with the performance when loaded with "fresh" components, but then he found a can of pre WW I DuPont black powder. Loaded with that, his .32 W.S. shot at higher velocity with less fouling and better accuracy, making it a worthwhile proposition for the handloader at the turn of the previous century.