There are three types of swords used in fencing...
a light, thrusting weapon, originally used for training soldiers to fight in battle. The target is limited to the trunk of the body, including the back but not the head or arms.
a heavier thrusting weapon, originally used for duelling, with no limit to the target area. One-hit épée is one of the disciplines of modern pentathlon.
a cutting and thrusting weapon, originally used for fighting on horseback. The target is limited to everything above the hips, except for the hands and the back of the head.
See the following Beazley sites for further information: