A University will typically offer undergraduate degree, graduate degree, and post-doctoral programs while a College will typically only offer undergraduate degree programs. Institutes on the other hand usually offer curriculums and degree programs concentrated on a certain discipline or a group of related subject areas. Examples can be found in institutes of Technology, the Arts, Architecture, etc.
Additionally, within universities and colleges, there are academic departments also known as Schools. Each school within these institutions is responsible for the degree programs in its area of study. Examples are School of Business, School of the Arts and Sciences, School of Education, etc.
For more information and other different types of colleges in the United States, please refer to this excellent slide made by Collegeboard.