You’ve got your kidnapping and dognapping that have to do with capturing either people or dogs. But then you come to catnapping and it means sleeping — except that in 1983 the London Daily Telegraph used it more like kidnapping: “Mr Smith..suggested that Tilley may have been ‘cat-napped’.”
Power napping is definitely sleep. But some kinds of cloth (velvet, for example) have a “nap,” which is a layer of thread that projects up away from the surface. In all, there are (or have been) at least 19 different versions of “nap.” In the 1400s a “nap” was a drink. In the 1800s a “nap” was a leg of beef, a fake hit or punch in the theater, and a card game. In the mid-1900s “nap” was used to mean a disobedient horse as well as any thick sauce that covers and adheres to food. I could go on.
The “nap” in “kidnapping,” though, comes from the 1600s and was probably imported from the Swedish, Danish and/or Norwegian “nappe,” which means to snatch or steal. It was originally used alone, like in this 1665 example: “My Chester-Landlord..espy’d me, and..presently fetcht two Officers, and coming out into the street napt me.” It only took until the late 1600s for “kid” to be attached: “A Servant, who was Spirited or Kidnapt (as they call it) into America” (1693). Kidnapping in those days generally meant abducting someone (usually a young person) and sailing off to the New World where they’d be forced to work as a servant.
The version of “nap” that means a short sleep is a different word, derived from the Old English “hnappian,” which meant the same thing. There was another Old English word that ended up as the (obsolete) “nap” that meant a bowl or cup, but they didn’t have to put up with the confusion we do, because back then it really was a different word: “hnæp.” The “h” in both cases is silent — maybe it was soundnapped. Or else it’s just napping.