State Bank of India was established before centuries, that is, during British Rule. It was known as Imperial Bank of India. Bank of Calcutta was established in 1806, Bank of Bombay was founded in 1840 and Bank of Madras was established in 1843. In 192, these three banks were amalgamated and named as the Imperial Bank of India. And after Independence in 1955 our Government changed the name of Imperial bank of India to State Bank of India.
According to Forbes, SBI is the 29th most reputed company in the world and it is one of the largest financial institution in the world.
State Bank of India is not a nationalized bank. Yes, you heard it right. It is a public sector Bank but not a nationalized bank. State bank was always owned by Government. In 1955, when the State Bank of India was formed, the Reserve Bank Of India owned the 60% stake of it. In 2008 Government took over the stake owned by Reserve Bank of India. SBI is controlled by State Bank of India Act 1955.
On the other hand, nationalized banks are those banks which were started and operated by private owners and after some time government of India through its act ' "Banking companies Acquisition and transfer of undertakings" nationalized them, acquiring more than 50% stake of those private banks. At present, there were 27 Public Sector banks and 19 nationalized banks in India.
Some of the nationalized banks offer better deposit rate than State Bank of India. But if you talk about loans, SBI rates are lower than any other bank in India. It is the largest public sector Bank in India.