You found them in 1701? Dang , you ol man you...L.o.l..
Small one is like a "bag" axe. Tote on a shooting bag. Multiple uses. Head by the head ,more finesse. Stout enough to split a pelvis or brisket or break bones for marrow.
Larger is close enough in style to be a shingling hatchet.
But....Depending on what was available , (wars changed trade and business and even cultures of who laid claim to a region) that sometimes you took what you could get for tools.
A time came when finding a tradition hawk (and multiple styles existed prior) was not a matter of convenience.
Just as there were times a blacksmith doing custom work was not handy.
Great recoveries Truth.
I handled a head decades ago and hunted with a long time. Since retired it. For now.
Never did get a solid I.D. on it. But , it's old and hand forged. That's enough I guess.