It depends. In some cases "for the sake of" and "for the good of " both mean in order to help someone/something. Example: we recycle for the sake of the environment or we recycle for the good of the environment. In other cases, "for the sake of" means because of. Example: Let's not argue just for the sake of it. (meaning let's not argue just because we can.) "For the sake of" could also be used to emphasize a request when you are impatient. Example: Hurry up for goodness' sake!