Hi everybody,What is difference among METRO,MARC and AMTRAK trains?

I'm guessing you're talking about Washington, DC.

Metro is a subway system that links downtown Washington, DC with the suburbs in Virginia and Maryland.

MARC is a commuter train system operated by the state of Maryland that mostly operates on weekdays, connecting parts of Maryland (in particular Baltimore) with downtown DC.

Amtrak is a US-wide train system that connects parts of the country. If you want to go from DC to New York by train, you would ride on Amtrak, which leaves from Washington Union Station.

metro stays in the city marc goes ll the way to philly amtrak goes everywhere else

Metro and MARC are just commuter trains which take people into and out of major cities to the suburbs where as Amtrak is a long distance train

Basically there is no real difference apart from their purpose. Amtrak provides long-distance services: depending upon the actual route the trains will have facilities such as first and second class travel (or whatever you call it your 'side of the pond'), refreshment facilities - possibly even full meals - sleeping compartments, observation lounges, toilets, and generally more-comfortable seating. So-called Metro/subway and similar trains are for shorter-distance mainly commuter traffic in and around cities. As such they usually only provide one-class travel, the seating is more basic, and even toilets are often not provided.