Public colleges and universities: Institutions predominantly funded by public means through a national or state government. Includes state land-grant universities.
Examples: University of California; Ohio State University; Century College

Private colleges and universities: Higher education institutions not operated by governments. Most private universities are non-profit organizations.
Examples: Stanford University; University of Notre Dame; Macalester College

Nonprofit: Most U.S. colleges and universities are not-for-profit institutions. Nonprofit schools can be pubic or private.

For-profit: The business model of these private institutions is to make money from providing educational services to students.
Examples: Capella University; National American University; Argosy University

Accredited colleges and universities: A school or program that has met the standards set by a non-government agency that reviews institutions in a region or occupation. Institutions accredited by the same agency are more likely to accept each other’s transfer credits.

References

• Types of College: the Basics (College Board)
• Types of Colleges (MyCollegeOptions.org)