The main hatchet axe difference is the size. Hatchet is a much smaller version of an axe, which can be used with only one hand and it is very handy for working on different woodworking and wood carving projects. Various types of hatchets can be connected to the same types of axes, only in a smaller size. Hatchet types vary in the shape of the head, the tips and the edges of the blade, as well as the length of the handle, its material, and whether it is curved or straight.