Would anyone know a general term for any language that is used by speakers of different languages to communicate with each other? (It is somehow related to the word "frank".) Thanks for any help.

You're thinking of a lingua franca. English is often used as a lingua franca today, as when the Austrian lady in my office uses English to talk to the Indonesians.

A pidgin language is different in that with a pidgin the two sides evolve their own ad hoc way of communicating using elements from both their languages (imagine the situation where slaves in the Americas from different areas had to communicate with each other).

A creole is different again. When people from different groups evolve a pidgin language and pass it on to their children as a native language, then it becomes a creole.

Bingley