As a concept, neither is a typeface. But in printed form, whatever consistent lettering you use to represent an alphabet is a typeface. Why should a printed/raised lettering for Braille be considered any different from a typeface printed for any other alphabet? Or typefaces for logographic writing systems, for that matter?
Braille (the concept) is not a typeface, just like the concept of representing certain sounds by pictures on paper is not a typeface.
Unified English Braille (the specification that maps dot combinations to English characters) is not a typeface, just like ASCII is not a typeface.
I Ould argue, however, that a specification like Marburg Medium[1], which specifies how Braille should be represented physically, how big the dots should be, how far apart they should be spaced etc, is a typeface.