A headsail, or jib. The only real difference between a jib and a genoa is the size. If the leech (back edge of the sail) extends beyond the mast that supports the mainsail, then it is a genoa.
Genoa is not so common, or important, a sailing term since you can call a genoa a jib, and still be correct. All genoas are jibs. However, if the sail does not overlap the main mast, it is inaccurate to call a jib a genoa.