Am example of a government corporation is:

amtrak

Post Office

Federal Deposit Insurance Corporation (FDIC)

it is a government corporation.

Federal Deposit Insurance corporation

"Public Corporation" can refer to a corporation that offers shares on the public market, or it can refer to a corporation that is owned by the government. Similarly, "Private Corporation" can refer to any corporation that is not government owned, or a corporation that does not list its shares on public share markets. A "crown corporation" is one that is owned by the government. This term is more widely used in UK, some Commonwealth countries and other monarchies.

A government corporation does a number of things but it is mainly tasked with the role of providing government services. This is a business entity which is fully or party owned by the government.