Ellipticals are some of the most popular cardio equipment in gyms and homes. But there is more than one kind of machine that bears the name "elliptical." Your local gym almost certainly has several elliptical cross-trainers and possibly elliptical trainers too, and there are also elliptical gliders. Some are commercial machines intended for gyms, and some are sold for home use.
An elliptical trainer machine is a lower-body-only cardio machine that has foot pedals you stand on and a stationary handlebar to hold onto. You use the machine by standing on the pedals and pushing on them to make circular, elliptical movements. Exercising on the elliptical trainer requires knee and hip extension, which works the quads, glutes and hamstrings.
The elliptical cross-trainer is a cardio machine that works the upper and lower body. It has the same pedal platforms as the elliptical trainer, and moves in the same elliptical pattern -- hence the name. The cross-trainer has moving arms that work the upper body as you push on the pedals; you push and pull on the metal arms in an alternating pattern to your feet. Instead of just targeting the legs through knee and hip extension, other joints that get worked include the shoulders and elbows. You also retract, or pull back, and protract the shoulder blades and collarbones when using an elliptical trainer to work your upper back and chest.
An elliptical glider looks very much like an elliptical trainer. There are stationary handlebars, no moving arms and foot platforms, or pedals. However, the pedals move up and down at a slight backward angle. They do not circle like elliptical trainers and cross-trainers. Elliptical gliders do, however, work the legs through knee and hip extension. You can pedal both forwards and backwards on the elliptical glider, as you can with other ellipticals. Resistance from the machine comes only from forward movement.
Ellipticals you see in gyms are commercial-grade machines. They're expensive -- typically thousands of dollars -- but are built to hold up to daily use from many users. Regular ellipticals for in-home use can meet your fitness needs just as well as the commercial-grade machines, however, and at a fraction of the cost.