Difference between public bank and a private bank and foreign bank?

Public bank: More than 50% stake owned by government. Hence controlled (management, operations etc) by govt.

Private Bank: More than 50% stake owned by private individuals or institutions within the country and registered in the same country. Private management.

Foreign Bank: Banks registered outside the home country and owned by individuals/institutions from Another Country but with branches present in home country. Has to follow regulations of both countries.