That distinction used to make sense as those different fonts with different sizes used to be physically different things.
With the advent of digital typography, that distinction doesn’t make any more sense. Typefaces can be seamlessly scaled up and down, there really is no longer even a need for an extra word for a typeface of a certain size. You don’t need the 12pt Helvetica Light file or the 9pt Helvetica Light file. Font and typeface became synonymous.
Now, given this history it makes sense to see typeface as referring to the abstract notion of the shapes of the letters and font to the technical implementation of the same, however, that distinction is hardly ever made and there is even factually no wide gulf between the two meanings. It’s one and the same and if you think it’s not, you are confused.