This article is from the Hanggliding and Paragliding FAQ, by Joao Geada with numerous contributions by others.
A Hangglider has a rigid frame maintaining the shape of the wing,
with the pilot usually flying in a prone position. The Paraglider
canopy shape is maintained only by air pressure and the pilot is
suspended in a sitting or supine position. The Hangglider has a
"cleaner" aerodynamic profile and generally is capable of flying at
much higher speeds than a Paraglider.