Financial Institution (FI) is an umbrella term that refers to the collection of institutions that are active in the (private and/ or public) financial markets.
A financial institution typically provides a wide variety of deposit, lending, and investment products to individuals, businesses, or both.
As the term covers a wide spectrum of activities, it is classified for regulatory, oversight, and other purposes.
A possible classification would be: central banks, retail and commercial banks, internet banks, credit unions, savings and loan associations, investment banks, investment companies, brokerage firms, insurance companies, and mortgage companies.