What they term in USA as Fed...?

The government of the United States of America - at the national level - is called the Federal Government. The way the US is set up, the states formed a Union (or Federation, though that word is generally not used).

You can trace the "Federal" part of it back to the 1700s, when the "Federalists" and "Anti-Federalists" were debating just how much of a Union the individual States should enter into. Originally, the US was incorporated under the Articles of Confederation, which implemented a loose Federal system - each State printed it's own money, and the only way the national government got money was if the states chose to donate money to it.

This, of course, didn't work out so well, and after about a decade, the Founding Fathers replaced the Articles of Confederation with the Constitution, which created a much stronger national government.

Thus, on a national level, the government is still referred to as the "Federal Government" to distinguish it from the various "State Governments."

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I am assuming you are referring to the use of "The Fed" in the financial press.

If so, "The Fed" refers to The Federal Reserve Bank of the United States. The semi-governmental organization that over sees the banking system in the US.