A depository institution is a non-banking financial institution (NBFI), also known as a nondepository financial institution (NDFI). It is a financial institution in the United States (such as a savings bank, commercial bank, savings and loan associations, or credit unions) that is legally allowed to accept monetary deposits from consumers. Under federal law, however, a "depository institution" is limited to banks and savings associations - credit unions are not included.12 U.S.C. 1813©.
An example of a non-depository institution might be a mortgage bank, which, while licensed to lend, it cannot accept deposits.
See also Authorised deposit-taking institution Shadow banking system Non-bank financial institution
References
Ruben D Cohen (2004) “The Optimal Capital Structure of Depository Institutions”, Wilmott Magazine, March issue.