Top left is a hewing hatchet, also called a side-hatchet or broad-hatchet.
The second one on left is a full hatchet with nail claws.
Third is a half-hatchet with nail claws.
Fourth is a full hatchet with a nail slot and pole.
Fifth is an old Boy Scout axe (from my grandfather's barn, I think). It feels good in even my large hands.
Top right is a checker-pole hatchet with a 19" handle. It probably started out as a 20", since this was one of my granddad's rig-building hatchets.
second is also one of Granddad's rig-building, checker-pole hatchets, but with a new 14" handle. You can't find 20's around here anymore, and I've never yet made one from scratch.
Third is the True-Temper pole hatchet I've had since I was a kid. Dad gave it to me used, even then (50 years ago).
Fourth is another regular pole hatchet.
Fifth is a regular pole hatchet, also.
Left 2&3, plus right 4&;5, I bought in Ohio's Amish country in times past. Left one, I bought locally at a now-defunct hardware store many years ago. Left 3 looks so much like a tomahawk, I think it would look good sticking in some hunter's belt. The head for left 4 was given to me by the old man that used to live across the road from me. ALL of the hatchets on the right side have nail slots. SOMEWHERE, I've got another Boy Scout hatchet with a straight handle that the old man across the road put in it many years ago. I guess I'm "over-hatcheted," but when I see a good OLD one cheap, I just can't resist!