Player supports a variety of robot hardware. The original Player platform is the ActivMedia Pioneer 2 family, but several other robots and many common sensors are supported. Player's modular architecture makes it easy to add support for new hardware, and an active user/developer community contributes new drivers.
Stage simulates a population of mobile robots, sensors and objects in a two-dimensional bitmapped environment. Stage is designed to support research into multi-agent autonomous systems, so it provides fairly simple, computationally cheap models of lots of devices rather than attempting to emulate any device with great fidelity.
Gazebo is a multi-robot simulator for outdoor environments. Like Stage, it is capable of simulating a population of robots, sensors and objects, but does so in a three-dimensional world. It generates both realistic sensor feedback and physically plausible interactions between objects (it includes an accurate simulation of rigid-body physics).
Since Stage and Gazebo are both Player-compatible, client programs written using one simulator can usually be run on the other with little or no modification. The key difference between these two simulators is that whereas Stage is designed to simulate a very large robot population with low fidelity, Gazebo is designed to simulated a small population with high fidelity. Thus, the two simulator are complimentary, and users may switch back and forth between them according to their needs.