Made some important changes...see altered quote.
or..
NTR - your wife/gf is fucking other dudes either without you knowing at all, or right in front of you, showing that she prefers other cocks.
NTI - some other dude is fucking your wife/gf with the aim of stealing her from you. (usually without you knowing)
NTS - you want your wife to be fucked by other dudes. You may or may not also want to get involved in the fucking.
(Despite confusion with the above, sharing and swinging are mostly their own thing, and not always any form of NTR at all. Its why swinging already has its own tag, and sharing should too imo)
Not arguing, just a different way of saying mostly the same thing, a few minor differences which can be important to some.
I disagree with you about the tag fetish; it's always defined from the main character's point of view, since you control him and therefore he "represents" you. (Pure VM: the player doesn't make important decisions, but the story is still being told from their point of view. I know that players can put themselves in the MC's place, as spectators, just pressing Ctrl, and others who take on the role of the NPC.)
The tags are meant to represent fetishes for the player, not a community, and we can divide them into categories: Story (Netorase, Netorare, Netori, Femdom, harem, romance, sharing, corruption...). They have their own culture and characteristics and can carry more than one integrated fetish, and are much more difficult to merge. In Netorare, the MC will be the "beta" cuckold with a small or pencil-shaped penis, while in Netori, the MC will be the "alpha" bull with a magical and enormous penis. This doesn't apply to sexual activity (vaginal, anal sex, masturbation, foot...) and characteristics (big ass, big tits, SPH, etc.).
All three are part of the NTR family; the first was Netorare, all others derive from it, which is why it's the most famous and we frequently use the abbreviation NTR to represent it, but it can also be used for Netorese (NTS) and Netori (NTI).
Netorare (NTR) isn't about whether the MC knows or not, since sooner or later he'll find out about the betrayal, but rather how he reacts to the feelings of loss, betrayal, hatred, anger, and jealousy—these feelings are all negative. The relationship continues out of hope of winning the woman back, blackmail, financial gain, or other reasons, with other fetishes being mandatory (humiliation, SPH, etc.).
Netorase (NTS) can begin with the MC encouraging or infidelity by the wife, but the difference lies in the feelings it awakens and the sexual excitement. Jealousy brings sexual pleasure; seeing her with other men excites him, etc. Some fetishes are optional (humiliation, SPH, etc.). The main point of difference is the MC's behavior.
Netori (NTI) is a role reversal where the MC is the "alpha" bull with a magical penis while the NPCs are the "beta" cuckolds with small or pencil-sized penises, the NPCs' wives have sex with the MC, and it is he who humiliates the other men; the MC is the "superior man."
But I agree that fetishes like swinging (partner swapping) and sharing (allowing for extramarital relationships), as well as open marriage (both involve extramarital relationships), are different fetishes and have their own characteristics, even though they are not traditional and, while they could be considered part of the cuckold culture, they are not part of the NTR family.