The difference between a precancel and an overprint is that an overprinted stamp is put on sale to the general public, and need to be cancelled when they go through the postal system to stop them being reused. Precancels were on sale only in bulk to companies which wanted to process large numbers of e.g. magazines or mail order catalogues quickly. They were simply handed in to the Post Office in the town named on the stamp and they were processed immediately without having to wait to be cancelled.The recipient could not soak the stamp off and use it himself because it was only valid when handed in to the named office by a representative of the company.
The Kans. and Nebr. overprints are unusual. Post Offices were suffering raids in which stamps were stolen and taken across the border to be resold. These two states put the state name on so if they were stolen they would immediately arouse suspicion if offered for sale outside the named state.
Anything (almost) other than a regular cancellation printed on a stamp is an overprint. Specific types of overprints are normally referred to by the name of the specific type like surcharge and precancel and then we have KANS and NEBR and Molly Pitcher and such that referred to just as overprint. Welcome to the secret language of the philatelist.