Different between private bank and governement bank

A bank in which Government owns more than 50% stake is called a public sector bank or a Government bank.

A bank where individuals or private institutions hold the majority of the stake are called private banks.

Examples of Government banks in India are

a) State Bank of India and it's associates
b) Nationalised banks like Andhra Bank, Allahabad Bank etc

Examples of private banks in India are:
a) ICICI Bank Ltd
b) HDFC Bank Ltd
c) Yes Bank