A body cord is a cord that connects the fencers weapon to the reel, or scoring system. The type depends on the weapon and style of plug.
Currently there are three styles as outlined in the picture below.
Epee is the most basic, and used only in Epee. It has three lines and matching plugs on both ends
2 Prong, used only in Foil, and currently the preferred format for that discpline. If you are fencing FIE only allowed format.
Bayonet, LP, or Leon Paul is used in Foil and Sabre. Since it is refered to as an LP in the UK, it becomes clear that Leon Paul created this format a while back. However, due to bad copies it has fallen out of favor in the last several years with the FIE and most clubs here in the states.