Leaning into the "meaning" I think is often going to be pretty close to mere colour, rather than fictional positioning.
That is how we approached stats in 4e D&D.
On the other hand, in our Classic Traveller game stats are also taken to establish fictional positioning, and so directly inform what actions are permissible and how they resolve (not just in mechanical terms).
Quite different ways of handling stats!
EDIT to also respond to this:
Mere colour is part of the fiction, but I'm focusing more on fictional position.
Like, in our Traveller game INT and EDU stats are taken to shape permissible action declarations, to shape resolution (independent of dice rolls - eg the ex-Navy officer with high EDU knows how to interpret naval codes). Likewise physical stats - the guy with high DEX and low STR is clearly small and wiry, and so could squeeze through the narrow space.
Sometimes stats also modify a roll in a mechanical fashion - but unlike in our 4e game, that's not all that they do.