The first question has to be, "What sort of design?" Generally speaking, options available at the college level include graphic design, fashion, commercial or industrial design and architectural design. The institutions offering extensive course and major selections in design tend to call themselves art and design schools. With that in mind, here is a list of the undergraduate (baccalaureate) degrees offered at one California-based school:
Advertising
Environmental Design
Film
Fine Art Media
Graphic Design
Illustration
Photography + Imaging
Product Design
Transportation Design
There are three degrees in this list dealing with still images. It would take a substantial discussion with a faculty member or advisor just to grasp the differences. Environmental design is related to architecture, but is more about the result of construction design than such things as load bearing walls and fire exits. Two majors that would probably qualify as industrial design, one is focused solely on transportation - building a better fender. Some of these degrees are Bachelor of Science, some Bachelor of Fine Arts.
These are fairly esoteric pursuits, to be defined at the college major level. Other schools no doubt have their own specialty orientations; if this one college is any indication the variables have fascinating possibilities. It is also interesting to see film and the fine arts mixed in with this assortment of commercial design professions.