I think your pieces are examples (maybe not all of them) of a Belt or Camp Axe.
From the Book "Swords & Blades of the American Revolution"
" Sir William Johnson estimated his need for approximately 10,000 in the Indian Trade just during the year of 1765 " (at the cost of only three shillings each) .
The VII Scottish battalion Co. 42nd Regiment (Black Watch ) all carried a wrapped belt axe.
Our American Rifleman 1779 all carried a cloth wrapped belt axe held in a loop sewn to his brown leather wastebelt.
Early Sources of Manufacture:
As French,Dutch,English and Swedish were founded here each Quickly recognized the need for axes and began importing on a major scale from northern Spain.
2 to 5 pound each referred to as" Biscay" axes or hatchets. Holland was another important source call "Utrecht" axes.
In America as might be expected demands in the new world led to modifications Smaller size, Weight and Balance led to smaller heads on the belt axe... popular used by 1720s weight under 2 pounds....large headed axes still held their place at the home and camp for heavy chopping.
Gary
Thanks for this book "Gare" much knowledge... i do appreciate it !