Amtrak has several types of equipment operating: Amfleet, Superliner, California/Surfliner, Horizon, Heritage, Viewliner, Talgo, Metroliner, and Acela.
Three types (Amfleet I, Amfleet II, and Metroliner) are based on the same body shell. They are single level and curved.
Metroliner: Originally bought by the USDOT for high-speed service under Pennsylvania and PennCentral. They were electrical multiple units and operated in pairs, with connection possibilities between pairs. A long time ago, they had their motive power equipment removed and were converted to cab-cars. You will see these operate on the Keystones and Springfield shuttles.
Amfleet I: Built on the same shell as the Metroliner, it was basically a Metroliner-coach, missing the drivers cabs on the ends, the electrical equipment, and having automatic doors plus the ability to use low platforms via folding stairs. They run all over the Amtrak system on short distance routes.
Amfleet II: A medium-distance car used primarily as a long-distance car. The Amfleet II was designed to be used on long-run day trains, like the Palmetto and Vermonter. Not having its long-distance Viewliner coaches built as planned, the Amfleet IIs were eventually shifted onto long-distance duty where they remain today. They differ from the Amfleet Is in having larger windows, a single vestibule with manual doors, and a larger seat pitch.
Horizon: This is what you call a stop-gap measure. Desperate for equipment, Amtrak piggybacked on a NJ Transit order, building some short-distance cars for California service out of commuter equipment. They have been no end of an Amheadache and run primarily out of Chicago, which is amusing since they are not good in cold weather. They aren't particularly stable at speed, either, which is why you don't see them running the Corridor.
Heritage This is a motley group of cars inherited from other railroads and converted to operate on head-end-power. The only cars still running of what was a fleet of over 1700 running cars are: 31 baggage cars so built, 34 coaches converted to baggage cars, 19 dining cars, 5 lounge cars in use on the Coast Starlight, 7 coaches and lounges sold to NCDOT, 3 sleepers used by the Inspector General's office, and a full length dome, or a total of 90 cars.
Superliner: There are two generations (one built by Pullman, the other by Bombardier) but there isn't anything exceptionally different about them. They are bi-level and designed for long-distance service, which the serve admirably on ALL long distance trains that do not server New York.
Viewliner: Originally intended to be a several-hundred-car fleet of baggage, baggage-dorm, coach, lounge, diner, and sleeping cars (plus possible Slumbercoaches) so far only 1 diner and 52 sleepers have been built. Everything I have heard so far, however, indicates that the Viewliner will become the basic shell for every single-level national fleet car. Currently there is an RFP for 25 diners, 25 bag-dorms, 50 baggage, and 25 sleeper cars, with options for more. However, I have heard about plans to order something like 500 short-distance coaches, 175 long-distance coaches, 75 cafe cars, 25 lounges, 100 cab cars, and 25 high-speed train sets based on the design- eventually these would replace the Amfleet, Metroliner, and Acela fleets.
Surfliner: A short-distance inter-city coach based on the basic Superliner shell.
Acela: Amtrak's high-speed train set.
Talgo: A unique group of cars used only on the Cascades.