--I didn't have my travel alarm clock, but I didn't need it, because I can use my cell phone as an alarm clock.
--I thought that I couldn't make the recipe, because I didn't have any maple syrup. Then I decided that I didn't need maple syrup, because I have brown sugar, and that's close enough.
There IS a usage in which "have" and "heed" can mean the same thing: "have to" and "need to." There really isn't any difference in meaning and I can't say how I decide which to use. (I speak U.S. English).
--I didn't have to pay anything, because my friend said I could be his guest.
--I didn't need to pay anything, because my friend said I could be his guest.