Jack 'O Lantern and headless horseman are two completely different legends.
The Headless Horseman was a revolutionary era Hessian Mercenary under the employment of the Brittish Crown. Killed in combat, his spirit was forced to roam the Earth as a revanant when he was beheaded and the head was hidden from him.
Some tellings don't include the flaming pumkin head.
Jack was a well known village trickster and joker who was even able to pull one over on the Devil himself. The Devil impressed by his trick, awarded Jack with a gift, a carved pumpkin with an eternal flame within it to serve as a lantern.
The Headless Horseman was a revolutionary era Hessian Mercenary under the employment of the Brittish Crown. Killed in combat, his spirit was forced to roam the Earth as a revanant when he was beheaded and the head was hidden from him.
Some tellings don't include the flaming pumkin head.
Jack was a well known village trickster and joker who was even able to pull one over on the Devil himself. The Devil impressed by his trick, awarded Jack with a gift, a carved pumpkin with an eternal flame within it to serve as a lantern.