Do any languages had different words and/or verb tenses for we “you and I” and we “other people and I but not you”?
This is known in linguistics as clusivity. Exclusive stuff excludes (obviously) what works out to be the second person, that is the person or people one is speaking to, while inclusive stuff includes them. Such a distinction appears in Hawaiian, making we as in “me and toi” kāua, while me and him or her is māua. Also of interest is that Hawaiian distinguished between singular, dual, and plural forms, so there is another set of wes, with “me and vous” being kākou and “me and them” being mākou. Clusivity applies in both the dual and the plural cases.
(Toi here is an explicitly singular you, and vous is explicitly plural, even though it doesn’t quite work out that way in French. It used to though, for what it’s worth.)