Here is a list from medieval times to when the death penalty was abolished. Records are not available for Headsmen earlier than this, though cutting a head off in one blow hardly happened: it took usually 3 to 10 blows.
An executioner is an agent of the state with a warrant to kill a criminal who has been sentenced to the death penalty.
They have been either Headsmen (beheadings) or Hangmen (hangings)