Gravestone, from the early 1300s, is an inscribed stone marking a grave; tombstone, from the late 1500s, is a flat, inscribed stone laid or standing over a grave (often acting as a lid) and has been used as a synonym for gravestone since the 1700s; headstone, from the late 1700s, is a slab at the head of a grave, usually inscribed. By now, all three terms have more or less the same meaning, with tombstone holding comfortable popularity over the other two.
However, if you’re determined to differentiate the three words, prefer gravestone for an inscribed stone marking a grave, reserve tombstone for the inscribed lid of a tomb (the sort of thing pushed aside in adventure movies), and abandon headstone, the least evocative and common of all three.