A typeface is something like Bodoni, Helvetica, Gill or Univers.
A font is a specific geometry within that face, like 9pt, or 10pt, or Bold.
Today the terms have become confused, with Adobe and Microsoft etc. selling what are really typefaces as "fonts".
In the era of steam railroads, steam ships and steam beer, type was generally applied by sign painters. While the good ones understood what a face was, they usually had their own painter faces, and used wooden patterns to pounce the general outline onto whatever they were going to paint, then eyeballed it.
If you ever want to watch someone who really knows typography, sit and watch a good stone carver.