The NJ Transit version had manually operated end doors (now automatic, like the ones you find on Amtrak) and automatic-operated exterior doors (like you find on Amfleet Is and Surfliner/California cars). The cars were always designed with centrally operated exterior doors, which is why the Amtrak version, which has the reverse (manually operated exterior doors, automatic interior doors, corresponding with more longer-distance operation) does not have stairway traps. On the NJ Transit cars, the stairs are covered over by a sliding door when the doors are closed. Lacking that door, the Amtrak version is always exposed.
The Comet I could only operate on low-level platforms, for it had no trap and had a lower door opening.
Comet I:
Comet IIs corrected that problem for service on lines other than the Erie Lackawanna (all low platform) such as the Northeast Corridor and North Jersey Cost Line, by using trap doors and a long sliding door covering the stairs. It was also, to my knowledge, the first car that could operate with its exterior door closed and its trap door opened- which really simplifies train operation. They were what the Horizon is based on and were built by Bombardier.
Comet II:
The Comet III was similar to the Comet II but had a pair of centrally located automatic exterior doors, similar to subway cars, which speed boarding at high level platforms, also built by Bombardier:
Comet III:
The Comet IV is an improved Comet III, the main difference is found in the cab cars, which do not have cab-side doors, persuant to the safety findings of a train collision in Secaucus, NJ. They are also Bombardier-built.
Comet IV:
The last car using the Comets basic shape is the Comet V. I'm not sure how technically related to the original series it is. The original Comets were built from Aluminum, and were built by Pullman-Standard, followed by Bombardier who bought out the design. The next set of cars, referred to as Comet Vs, are very different. They have much larger windows, their air conditioners are located on top of the car, rather than in the roof, and they are built out of stainless steel. They are also built by the Anglo-French company Alstom rather than the Canadian Bombardier
Comet V:
Their replacement is entirely unrelated, its a bi-level car sometimes referred to as the Comet Multi-level. I think NJ Transit has refrained from this practice, which makes sense- it isn't related to the comet in the slightest: