They are very difficult to tell apart.
I 'think' I can tell in person, in my yard, but don't know technically any hints for you. Rose of Sharon self seeds a lot under itself, around here. I pull all my rose of sharon seedlings, it is so common and not my favortie, so I let someone else worry about sharing them with other gardeners.
I don't find mulberry seedlings under that tree, but do have them also under shrubs- where birds sit.
So- under Rose of sharon= think same
everywhere else= think mulberry