Adam Clarke on Judges 8:33

A whoring after Baalim - This term has probably a different meaning here from what it has Jdg 8:7; for it is very likely that in most parts of the pagan worship there were many impure rites, so that going a whoring after Baalim may be taken in a literal sense.

Baal-berith - Literally, the lord of the covenant; the same as Jupiter faederis, or Mercury, among the Romans; the deity whose business it was to preside over compacts, leagues, treaties, covenants, etc. Some of the versions understand it as if the Israelites had made a covenant or agreement to have Baal for their god; so the Vulgate: Percusseruntque cum Baal faedus, ut esset eis in deum.