I've played 1e, 2e, 3x, 5e, PF1 & now PF2 - some of them on alternating weeks/days (there was a span where I was involved in a bi-weekly 1e game on Tue, 5e on Thur, & PF1 on Sunday).
Rather than shift gears terminology wise I'd just ask for whatever type of save or skill check rolled of the tongue 1st & leave it to the players to decipher. Still do.
It throws some of the younger players (or those who only know one system) for a loop. But my fellow veteran players know exactly what's going on: If you could see inside our heads? It's just a soup of 30some years & 5-6 editions of very similar rules.... But at least with D&D, pick one & odds are you'll know easily enough how to apply it no matter what the edition.