I wasn’t completely clear on their usage, so I googled it, and this was the best result:
the physical embodiment of a collection of letters, numbers, symbols, etc. (whether it’s a case of metal pieces or a computer file) is a font. When referring to the design of the collection (the way it looks) you call it a typeface.
When you talk about how much you like a tune, you don’t say: “That’s a great MP3”. You say: “That’s a great song”. The MP3 is the delivery mechanism, not the creative work; just as in type a font is the delivery mechanism and a typeface is the creative work.
font is what you use, and typeface is what you see.
This is probably one of those things that drives graphic designers crazy. But, outside of design studios, the language has become much more relaxed. This is just another one of those cases where the meaning of the word changes to account for relaxed usage.