What is a bank owned by the state and operates nationally called?

A national bank is defined as a financial institution that is chartered and regulated by the federal government. It operates under federal laws and regulations, which allows it to engage in banking activities across state lines. National banks are members of the Federal Reserve System, which provides them with access to federal resources, including the ability to issue currency and participate in the wider economy on a national scale.

The designation of "national" indicates that the bank is not limited to a single state or local area, but rather has a broader operational scope, allowing it to serve customers nationwide. The other options refer to different types of banking institutions. For instance, a state bank operates under the laws of a specific state and may not necessarily have national reach. Similarly, the Federal Reserve is the central banking system of the United States, not a bank in the commercial sense, and private banks are owned by individual shareholders or corporate entities, focusing on profit rather than being overseen or operating under national regulations.