Like the name suggests, when you do stiff leg deads, you keep your legs locked (although knees are still slightly bent). In the regular dead, you bend your knees and use your legs more.
I do them both. Stiff on leg day (to work hams), and regular deads on back day. I actually prefer stiff leg deads, and I do them on a raised platform, that allows me to lower the bar almost to my feet. You get a great stretch in the hams, and you'll be feeling it the next day.