According to Wikipedia, "Paragliding is a recreational and competitive flying sport. A paraglide is a free-flying, foot-launched aircraft. The pilot sits in a harness suspended below a fabric wing, whose shape is formed by its suspension lines and the pressure of air entering vents in the front of the wing."
And again according to Wikipedia, "Parasailing, also known as par ascending, is a recreational activity where a person is towed behind a vehicle (usually a boat) while attached to a specially designed parachute, known as a parasail. The boat then drives off, carrying the par ascender into the air. The sheer power of the boat is powerful enough for 2-3 people to parasail. The par ascender has little or no control over the parachute."
Your level of interest helps you decide whether you would choose to go for paragliding or parasailing. Those who yearn to be in the driver's seat, with a sense of adventure and knowledge of his or her limitations, should take lessons to become a paraglide. The laid-back ones who prefer others taking charge should hold onto parasailing. Both the activities are a great way to relax and unwind.
The first and foremost difference between parasailing and paragliding is that - Parasailing is for those who love the water but do not prefer extreme endeavors such as jet skiing or knee boarding. Paragliding on the other hand is for the light hearted.
You can paraglide nearly anywhere but mostly Para gliders choose open fields, exciting cliffs and mountain ranges for their intense scenery. Parasailing on the other hand is done on big water masses and sometimes on land as well all with the safety and security of a parachute.
In parasailing, you need a motorized vehicle and a canopy to make you airborne whereas in paragliding wings are controlled solely by the rider, who is technically a pilot.
Another obvious visible difference is that parasailing is a team effort while Paragliding can be done solo. Even the manner in which one is lifted off differs in parasailing and paragliding. In paragliding you are propelled by parachute if you're on land or a backpack if you have opted for powered paragliding.
Before you go parasailing all you need to do is take a few minutes of water safety lessons. However, in paragliding you need to take a few days training before you can go for a solo flight.