So these are your own personal definitions, but I'm categorically wrong?
IMO the term "NTR" is one of those things that should never have been adapted into English because I don't think there's really a good translation. As a result it gets used liberally to mean just about anything. From what I've gathered when reading about it, there needs to be an element of humiliation, and powerlessness to the arrangement. Swinging, hot wifing, and even cuckolding, wouldn't count because the boyfriend/husband is willingly entering into the arrangement. They accept that they find sexual gratification in the arrangement and encourage their partner. A cuckold will jerk off to the idea of his wife getting fucked by another man while she tells him how inferior he is.
But with NTR the boyfriend/husband doesn't enter into the arrangement willingly. And, unlike a simple "cheating" tag, for one reason or another he can't easily extract himself from the situation. So you have a boyfriend that can't/won't break up with the girl (maybe he doesn't have definitive proof, or he's ignoring the obvious, or he's being blackmailed) and hates himself for begrudgingly enjoying his girl fucking another man. It also seems really necessary for the woman to absolutely disregard his feelings, whereas a cuckold's girlfriend will still have a loving relationship with their boyfriend.
In practice this gets really messy because NTR lives in the grey area. To a large extent NTR is in the eye of the beholder.