I'm in the midwest, I putter about the house completely aimlessly. Cars putter along the road.
Dithering to me is a mental thing. You dither about whether to wear the red shirt with the black pumps or the black dress with the ballet flats when you go out at night.
Futzing, to me, is unnecessarily messing with. For example, if I'm puttering about, I might fold a few towels, go to wash a few dishes, just basically wander around aimlessly doing random things for a tiny bit before moving on to something else. If I was futzing about the towels, I'd unfold all of the towels in the house just to get them right.