In our experience riding Silver Star and Meteor, your destination does determine which coach you end up in, with long-distance passengers in different coaches from short-distance passengers. When the train arrives to pick you up, a crew member asks what your destination is and how many are in your party, and directs you to the appropriate coach entrance accordingly, or if you are at about the right coach, he or she will assign you the seats you are to use. He or she will usually have a card in hand that shows the seats currently unassigned and will make a mark on the card showing those seats as now assigned. . At some stations, where there is a large number of boarding passengers and more than a couple of minutes available to do it in, the conductor will go into the station and check-in the passengers at a desk or at the door. At most stations, though, they just stand at a coach door and the passengers just line up to board.
For short-distance passengers on SIlver Service (that is usually our category, traveling mostly from one place in Florida to another), they usually don't bother putting destination tags over the individual seats. I expect that in the long-distance-travel passenger areas, they are more likely to do that.
You are indeed allowed to roam the train, at least as far as the diner (for meals). Forward of the diner is off-limits to coach passengers, as that is where the sleeper cars are, which is only for first-class passengers. But from the lounge car on back, feel free to wander. I would recommend, though, that during short station stops, you remain seated either in the lounge (or the diner, if eating a meal), or in your assigned seats, as there will be passengers trying to either board or exit the train, and you could end up impeding that if you are wandering around then. Anything that impedes work at a station stop helps make the train late, which none of us wants!!.
The usual make-up of the Silver Star or Silver Meteor trains (in order) is: an engine, a baggage car, a dorm car (for the on-board service crew), two sleeping cars (for first class passengers), a diner, a lounge/cafe car (snack bar plus tables to munch at, play cards visit, or whatever), and then four coaches. Depending on season and passenger load (and car availability) it could have one more or one less baggage, sleeper or coach. The make-up of a particular train is called the "consist". Think of it as what combination and number of cars does a particular train "consist" of.
And have fun!!! We always do.
