Sometimes these subjects come easily, flowing out of discussion in another place. This bit of knowledge comes courtesy of Eric Pearson whose question was quite literally "What does nuki uchi mean?".

nuki uchi ( 抜き打ち) is to draw from the scabbard and strike in a single motion; as nuki tsuke ( 抜き付け) is to draw from the scabbard and cut in a single motion.

Generally, cutting has a sliding or slicing component to movement of the sword where striking does not. This is the same as slicing versus chopping in the kitchen (if you cook).

Thus, a strike is more powerful/definitive/committed but requires a withdrawal and reset of the blade. A cut is weaker but is not a singular technique, so that additional cuts or strikes can quickly follow.

This is the true difference that defines nuki uchi. Your initial posture; the angle or direction when drawing the blade; and target area of the body; are essentially irrelevant.