It’s weird but they are all different. I’ve never had an issue where I see an Xbox X and hit the PS X. Normally if a game wants X(PS Flavour) the X itself is blue, potentially with a black circle around it. If a game shows you an X(Xbox Flavour) it shows a blue circle with a different blue X inside. Nintendo generally just shows a top button glyph or if they do show the X it’s usually monochrome, except for Americana flavoured SNES which was just top purple and since GC had the vertical kidney bean X… Well, Nintendo only recently became a problem I suppose.

So, basically, the in-game glyphs do differentiate themselves.