Monetary financial institution
Monetary Financial Institutions (MFIs) are central banks and other institutions whose business is to take deposits and/or close substitutes for deposits from entities other than MFIs and, for their own account (at least in economic terms), to grant credits and/or make investments in securities.
In many contexts, MFIs exclude central banks.
For example, the Bank of England publishes statistics under the heading "Monetary financial institutions (excluding central bank) balance sheet".
But conversationally and informally central banks are taken as being "MFIs".
Here as elsewhere, consistency and transparency of definitions are essential for the avoidance of doubt.