Reserve Bank of India is the Bank Controller, the Big Daddy of all banks in India.
Its job is to issue policies, control and monitor the functioning of the banks as well as keep an eye on the liquidity as well as inflation aspects of the economy.
The State Bank of India, on the other hand, is the largest bank in India, with thousands of branches in India and abroad. The Government of India is the largest stakeholder in this bank, and it is one of the top banks in Asia. It's a regular bank like any other.