UPDATE: I descended into the basement to retrieve my copy of Cleeton, Pitkin, and Cornwell's General Printing, 3rd edition, 1963. (Back then Glen U. Cleeton was the Dean of the School of Printing Management at the Carnegie Institute of Technology, better known today as Carnegie Mellon University's College of Engineering.) Anyway, one sentence from the book makes it clear:

"A font is an assortment of one size and face of type."

In other words, most faces came in multiple sizes, and each face-size pairing (that you could buy) was called a font. A.T.F. Goudy Bold, to use an example from the book, came in the following sizes: 6, 8, 10, 12, 14, 18, 24, 30, 36, 42, 48, 60, 72, and 96 (all units given in typographer's points). Complicating the matter was that each font had a slight variation of the face design to accommodate the way that ink behaved on the type differently and was interpreted by the human eye differently at different sizes.