Amtrak, officially called the The National Railroad Passenger Corporation, is a corporation that was chartered by the U.S. government in 1970 (operation began May 1, 1971). The federal government owns the majority of the stock (source), but despite this, Amtrak is classified as an independent agency.
Other things to know: Amtrak has a Board of Directors that is appointed by the President of the United States, as well as a CEO and President. Additionally, Amtrak gets funding from multiple states and the federal government.