This is the main railway service on the Long Island. All the Lines terminate at several station which include

1. New York Penn Station

2. Jamaica Station

3. Atlantic Terminal

4. Grand Central Terminal (by the new East Side Access, not all lines go to GCT)

So one train line might have several destinations, it is alway best to check beforehand to see which station is nearest to your journey destination.

This is about the inter-city service. Amtrak's Northeast Regional is a high frequency service service basically every major city in the Northeast areas. 

Many people live in one city and work in another, for example some people live in Washington DC & work in New York City. This is known as supercommuting . This is a common practice done for family, money & a few other factors. The train helps these type of commuters to smoothly travel long distances.

This is a super important railway system for the thousands of Residents living in Connecticut & New York Upstate and working in the city. It is best adviced to not use the train during the Morning and Evening times as it is the time people are going and coming back from their work in NYC.

The icon of New York City, those grey metal trains criss-cross the city making it convenient to travel short in-city distances by the subway. The subway lines are very different from other metro systems, one line splits in 2-4 smaller lines, always recheck which one is best for your need.

The NJ Transit is probably the most busy railway in the NY/NJ Metropolitan area. It has lines only covering the North NJ City suburbs and 1 Line from Philadelphia to Atlantic City which is separate. The sole purpose is for the commuters who work in NYC & live in New Jersey.