While even I use the terms loosely, these are the correct definitions:
A "typeface" refers to a complete family of individual "fonts". So, the latter belongs to the former. For example, Helvetica is a well-known typeface, but it is made up of several fonts: for example, in different weights (thin, light, medium, bold, etc), or widths (condensed, extended, etc).
So, Helvetica is a typeface, but Helvetica Light Oblique is a font.
