By means of a secret charm, to draw
All creatures living beneath the sun,
That creep or swim or fly or run,
After me so as you never saw!
And I chiefly use my charm
On creatures that do people harm.
-Dr Radovan Karadzic
First off, it needs to be stated that there is a difference between Hags and Witches. Witches in popular and obscure folklore references humans (male and female) with magical powers. How they come by these powers vary tremendously from culture to culture, and in different times.
Holdovers from older faiths, witches (in the old world) were the often misunderstood practitioners of ancient ways of magic. Practitioners of these old faiths had to hide their activities to one extent or another, so there was ample ground for paranoia and misunderstanding.
Hags on the other hand are rather different creatures, though with many parallels and connections. Hags are not human beings but holdovers from ancient female mother goddesses. Many such religions had an all female priesthood who were often quite voracious in their appetites for sacrifice (notably male infants and men).
Much like Ogres and Trolls were degenerated Titans, Hags are degenerate fertility goddesses, nymphs and similar beings. They always appeared as elderly women, but were predators of the most dreadful sort. They used their appearance to snatch away children and to slay the strongest men with their terrible claws and fangs.