In selecting a typeface, you're also necessarily selecting the font, so why make the distinction?
From an artistic and technical point of view I get it, but from a user perspective the two are not separable quantities.
No, the reverse of that. A typeface of the overall look, a font specifies the size and things like bold, italic.
So what is commonly called the font is really the typeface, and what is called the size is actually the font.
Back when fonts of a specific size were physical thing this mattered a lot - you only had a limited number of fonts for each typeface.