We also use 'heel' (come sit at my side), 'in front' (come sit in front of me), 'mine' (drop / leave whatever you've got, handy when she's picked up something she shouldn't) and 'no more' (stop what you're doing), as well as the usual sit, drop, stand, stay, wait, come, leave it (leave the other dogs alone), watch me (look at me instead of the distractions), paw (stand there and don't move while I touch / pick up your feet), high five, shake, off, up etc.
With stay and wait, the way we learnt to distinguish between the two and to not confuse the dog is that stay is you going back to your dog and wait is calling your dog to you (or giving them another command).
I taught off and up at the same time with Juno by having treats and luring her on to things and saying 'up!' and luring her off things while saying 'off'. There's probably a quicker process but she learned it over time so that's all that matters. (: