Not exactly. Parachuting involves the use of a Dome Shaped piece of Nylon (or silk) which allows a smooth drop from the sky. Skydiving usually uses a rectrangular shaped Nylon shroud that allows a more GUIDED descent by pulling on the cords on either side. Also, in Skydving, usually free fall is allowed for the greater part of the distance down. It is the diving in free fall that is so exciting.

A performance as Google dictionary states: the sport of jumping from an aircraft and performing acrobatic maneuvers in the air during free fall before landing by parachute. "It is similar to the maneuvers I perform in freefall while skydiving ."