HEIs is a general term used for education institutions that do not have a university title.  However, as with universities, they provide courses that lead to qualifications including HNCs, HNDs, degree courses, and postgraduate courses. HEIs is also commonly used when talking about universities and HEIs as a group.

Are post-secondary institutions recognized as bona fide in their home countries. In the United States, recognition is by accrediting agencies recognized through the U.S. Department of Education. Norma [..]

an establishment providing higher education and recognised by the competent national authority of a participating country as belonging to its system of higher education.

institutions operating under the provisions of the Act of the 27