You ain't the only one. I have the same headcanon of them not being the same.
I headcanon Hyperdeath Asriel(nicknamed "Asier" to keep him and Asriel apart) to be more of an angry/salty, british(speaking-wise) Asriel with a knack for making bad jokes, creative insults for anyone including himself and being the "overprotective older brother" of Asriel, Frisk(I see them as a girl) and Chara(Chara, too, is alive in my headcanon and I also see them as a girl.)