A rig is the whole parachute assembly worn on a jump — the harness that holds it to the body, the container on the back, a main canopy, a reserve canopy, and in most cases an AAD.
Two parachutes, always
Every sport rig carries two canopies. The main is what you use on a normal jump and can be packed by the jumper. The reserve is the backup, and in the U.S. it may only be packed and inspected by an FAA-certificated parachute rigger, on a regulated repack cycle.
That division is the reason riggers are a distinct trade within the sport, and why a rigger on site is a genuine convenience at a drop zone.
Student gear versus your own
Students jump drop zone equipment, which is typically larger, more docile and fitted with an AAD as standard. Buying a rig usually comes later, once jump numbers and canopy size have settled.
These pages explain what things are so the language makes sense. They are not instruction and cannot substitute for it — skydiving is taught in person by rated instructors at a drop zone, and anything involving equipment handling or emergency procedures belongs there rather than on a web page.