Type designers are sometimes mistakenly called fontographers. Fontographer was the name of a popular computer program for designing type, predominantly used during the 1990s and early 2000s.
Relationship to typography.
Typography is the craft of using pre-made Alphabets in designs, type design is the art of crafting new alphabets. Quite often one person occupies both roles, and specializes to a greater or lesser degree in one or the other.
See also How-To