Can you give the context in which you heard/read the two with orange? They are not fixed expressions.
Usually I hear about people "falling off the wagon" rather than being "on the wagon," but to me the difference is that someone who needs to be "on the wagon" has a problem with alcohol and is trying to quit, while a tea/teelltotaller will have nothing to do with alcholol at all. I suppose once you are firmly on the wagon, you're a teetotaller as well. I think of a teetotaller as avoiding alcohol for religious or moral reasons.