I think this is pretty much the gist of why it's different. In 5e tgey made a big show about how it was an ability check and you applied the ability score mod relevant to what/how you were doing it... then they wrote everything suggesting that skills only ever had one ability and put a cherry on top of that schizophrenia by adding the already mentioned "VARIANT: skills with different abilities" for the critical mechanic needed to actually have:"ability checks".In core 5E no. You use one ability and one skill like it says in the rules on ability checks.
In A5E dunno, nobody’s seen the rules yet, but I would guess no.
I'm on my phone right now but seem to remember reading that the ability score wont be mentioned alongside the skill but specializations would be listed. Take the proficiency bonus (or whatever -- if proficient)add your expertise die as relevant and add the ability mod the GM agrees or outright states fits best seems likely