They're not different at all. Yes Mugler is his brand. I'm guessing the person tried to say that she was working with Formichetti and not Theirry Mugler, but it's still the same really.
!!!! people kidna forget that RedOne is the person who brought us Just Dance, Poker Face, LoveGame, Bad Romance, Scheisse and Hair
While he did and that's great. He's managed to wear thin on his own productions. I don't think Gaga is going for that sound anymore. I'm sure she still respects him and his work though. And honestly I wouldn't be surprised if they snuck in one of his productions for ARTPOP. I just think they grew apart musically.