All three are genuine, recognised universities — but how they came to be one, and what that means practically, differs.
Central University
Established by an Act of Parliament and funded by the central government (examples: Delhi University, Jawaharlal Nehru University, Banaras Hindu University). Central Universities are relatively few in number and generally have national-level intake and reach.
State University / State Private University
A State University is established by an Act of the relevant State Legislature and is typically state-funded. A State Private University is also established via a specific state Act, but is privately funded and run — and per UGC regulations, its operations (including offering programmes) are generally expected to stay within the boundaries of the state that established it, unless it has specifically approved off-campus centres elsewhere.
Deemed-to-be University
An existing institution with a strong track record can be granted "Deemed-to-be-University" status by the UGC/Ministry of Education under Section 3 of the UGC Act, giving it university-level autonomy (its own curriculum, exams and degrees) without a dedicated new Act. Many well-known private institutions, including several major medical and technical institutions, hold this status.
Why the distinction matters to a student
The category itself isn't a quality signal in either direction — strong and weak institutions exist in every category. What it does affect is things like geographic reach (a state private university's main campus operating only within its home state), governance structure, and sometimes fee-setting flexibility. Always evaluate the specific institution's own track record, faculty, recognition and accreditation rather than assuming one category is inherently better.