Hey as per my idea SBI is state bank of India and SBBJ is state bank of Bikaner and Jaipur and here I am giving you its details

History of SBBJ
State Bank of Bikaner & Jaipur came into existence on 1963 when two banks, namely, State Bank of Bikaner (established in 1944) and State Bank of Jaipur (established in 1943), were merged.
Both these banks were subsidiaries of the State Bank of India under the State Bank of India (Subsidiary Bank) Act, 1959.
On 25 April 1966 SBBJ took over Govind Bank (Private) Ltd., Mathura,[5] established on 8 February 1963.

History of SBI
State Bank of India is an Indian multinational, public sector banking and financial services company.
It is a government-owned corporation with its headquarters in Mumbai, Maharashtra.
As of 2014-15, it has assets of INR 20,48,080 crores and more than 14000 branches, including 191 foreign offices spread across 36 countries, making it the largest banking and financial services company in India by assets.

Main difference between SBI and SBBJ
Main difference between SBI and SBBJ is that SBBJ is associate bank of SBI