According to www.tartansauthority.com
I QUOTE" Halbard
The halberd or battle-axe was a Swiss invention which was a combination of spear and axe on a long handle. It was a direct descendant of the old Gallowglass two-handed, 12 inch bladed axe and was particularly effective against horsemen since the foot soldier could cut and thrust with it.
The 1881 Ancient Scottish Weapons had this to say on axes: The Axe is one of the earliest of weapons. The war-axe of iron, in its earlier forms, differed in no respect from the same implement used as a tool. The earliest form of the weapon-tool is a common axe-head longer and narrower in the shank than those now in use. Such axes are depicted as weapons in the Bayeux tapestry. War-axes of a later time were furnished with prolongations in the line of the shaft and hammers or spikes on the hack of the blade. The Jedburgh Staff was a long-handled axe with a curved or crescentic blade, with or without a back-spike. The Lochaber Axe had an elongated blade usually rounded at the upper end, and the staff was furnished with a hook on the end.
The axe and "broggit staff" appeared in 1425 as the equipment of those who were not archers. In the weaponshaws of 1535 halberts appear along with two-handed swords. The Lochaber Axe and the Jeddart Staff appear in 1643 in company with the broadsword. In 1647 it was appointed that seventy-two men in each regiment should carry halbards, and in 1650 Lord Lorne requests a supply of partisans, from the store at Aberdeen, for the equipment of his regiment of Life Guards''.UNQUOTE.
Another quote from the web clears up the names as Jeddart staff and added names below..
The Jeddart staff (also Jedburgh or Jedwart) is a polearm of the 16th and 17th centuries with a glaive-like blade which is fixed to its haft by two sockets, in the manner of a bardiche. Form D in the Caldwell classification.
I might add ...The nomenclature of Scottish axes, in particular, is confusing, and texts sometimes follow the classification scheme proposed by David H. Caldwell in his 1980 paper "Some Notes on Scottish Axes and Long Shafted Weapons".