Does intending one mandatory cause for ghusl suffice for another unmentioned cause?

Primary text

If one of the two mandatory causes for ghusl is intended, or if a woman intends ghusl for menses but not for janabah, there are two scholarly opinions on whether it suffices for the other. One opinion holds that it suffices because it is a valid ghusl performed with the intention of fulfilling an obligation, like intending to permit prayer. The second opinion holds that it suffices only for what was intended and not for what was not intended, based on the statement of the Prophet (peace be upon him), 'Indeed, for every man is what he intended.'