I usually use the terms font and typeface as it is summarized nicely in this FontFeed article. http://fontfeed.com/archives/font-or-typeface/
As a result, there can be cases, where the term typeface is applicable, but font is not. I wonder if there are cases for the other way around?
In German and according to my use that is the case. The German word for typeface is “Schriftart”, which has the meaning of “the written word” in it and as a result, I would avoid the term for the design of a dingbat font for example, since there aren’t any letters in it. But I am unsure whether this is similar in English. What do you think?