Beading needles are very thin and flexible. They are normally used for seed bead work. The eyes of the needles are the same width as the rest of the needle, so it is much easier to pass through seed and other small-holed beads.
Twisted beading needles are normally used for stringing beads because they do not have a sharp point to them. The wide eyes are easy to thread and they will collapse once you pass through the beads.