As far as my vague memory goes, 1.21 - 1.23 levels won't load in 1.20 in the same manner as TSF levels won't load in 1.23. In online play, 1.20 can't join with any other version than it's own, as well as non-1.20 players not being able to join your 1.20 servers. Of course levels saved with 1.20 are perfectly compatible with 1.21 - 1.23 and TSF. Aside from curiosity there's no good reason to use 1.20 as you're pretty much isolated and missing the Trigger Zone event.

1.20 was the version originally released by Project2 in EU/AUS while 1.21 was released on disc by GODGames in the US.

1.21 was never released as a patch as far as I know. 1.22 was a Jazz2.exe-overwrite patch, while 1.23 actually came as an installer-like patch that conveniently patched whatever you had installed as long as it wasn't one of the OEM versions.