The four broad categories
Government colleges are run by central or state governments, with the lowest fees and seats allocated mostly through AIQ and state quota counselling.
Private colleges are run by private trusts/societies under state government or university affiliation, with counselling-allocated seats (state quota) alongside management and NRI quota seats that follow separate, college-specific processes.
Deemed universities have university status granted by the UGC and run their own admission process under NEET UG, typically through a centralised counselling round distinct from state processes.
State-quota seats exist within a mix of government and some private colleges, reserved specifically for candidates meeting that state's domicile criteria.