Do you want to be a trained dancer or have general knowledge about dance?
The differences begin at the admission stage. Conservatories almost always require auditions. The next difference is in the curriculum. In general, college dance (or theater or music) majors are designed to give students a general overview of the discipline along with general education requirements of math, English, history, etc. The dance classes usually make up about one third of all the courses the student will take. Conservatory programs, on the other hand, are designed to train students in the discipline. Usually two thirds of their requirements are dance classes and the remainder are general education requirements. The other difference is in what is expected of students. Conservatory students, for example, have very rigid requirements about attendance and participation. However, if you miss a handful of classes as a dance major, no one will kick up much of a fuss.