There were a lot of variations on the murder hand. Sometimes an evil limb would kill other people because they knew no one would believe a ghost hand story from the guy whose fingerprints are on 50 dead necks. Other times, instead of taking control of your hand, little men would form on it and torment you. And it wouldn't be that unusual for a hand to sneak off and solve its own murder while you slept.
I don't think these similar evil hand stories came from laziness or creative bankruptcy. They were all heartfelt iterations on an idea everyone agreed was bone-chilling enough to be imagined a thousand different ways. I guess when you're away at war or at home reading a comic book, an out-of-control hand is both a physical danger and a betrayal by your only lover. Holy shit, it's an enemy with your exact strength that knows your most carefully guarded dick, nose, and ass secrets!