Ah, and in an area where this becomes somewhat more confusing -- probability -- I found that describing everything in terms of stochastic "experiments" and then talking about random variables corresponding to some values observed during the experiment is the least confusing approach.
The area where IMO we don't have good terminology for this is partial differential equations. There, we very often talk about curves through some space and functions applies to e.g. the point the curve provides and its tangent. We sadly create a ton of confusion by not naming the arguments to that function (rather using `curve(t)` and `curve'(t)` in their place). I think this is an area where talking about (in)dependent variables is a reasonable crutch for the ambiguity that's typically introduced.