Are there any other train services like Amtrak that offer interstate travel?

No, it's amtrak or bus.

The official passenger train service in the U.S. is Amtrak.. there is no other.

one light rail does st Louis light rails services two states
as the DC metro subway (it several Maryland and Virgina )
then we got the metro -north goes into Connecticut

Amtrak is a federally-chartered corporation established to provide interstate passenger train service in the U.S. It was set up in the late 1960s, when it became apparent that the railroad companies were abandoning passenger train service. As part of the deal with the freight railroads, Amtrak agreed to take over their passenger trains. The federal government provides a subsidy to Amtrak to make up the difference between what they collect in fares and what it costs to operate the trains.

There are a few instances of passenger trains not operated by Amtrak, but they consist of such things as commuter trains, tourist trains, and dinner trains.

In a nutshell, if you want to go from city to city in the U.S. by train, the only option is Amtrak. You can get a copy of their system map, showing which cities they serve (they don't go everywhere), by going to their website:
http://www.amtrak.com

Don gave the best answer in this case.

I can tell you from experience that Amtrak does a pretty good job handling their customers.

My wife and I travel on Amtrak twice per year. I have had no complaints with the staff, accomodations or the food on the train.

As I have mentioned though, they could work on their timelyness a little more, but that is another story for another time. Just suffice it to say, that when you ride Amtrak, its best to not be in a hurry getting to where you go. For that reason, my wife and I add 2 extra days to our travel plans to allow for the train trips at either end of the vacation, (One Day's Travel Time, Arrival and Departure).

Depending on the route you are intending on, I would strongly suggest that you bring your camera. Once you are out of the city or urban areas, you are going to see scenery that you cannot see from a car. Plus the windows on the train are huge, so taking pictures is a real treat!

Enjoy your trip!

Sorry, no. The only interstate rail service is offered by Amtrak.

This is off topic. I peeked at your pics., and I think your prom date should consider himself to be a very fortunate young man to have such a charming date.

Amtrak is the only interstate train service in the United States.