Imho sharing and especially swinging aren't really the same thing as (the definition most people have of) cuckolding. Cuckolding is often associated with 1.not participating 2.humiliations. So while cuckolding is a part of what we call sharing, I don't think that term is used the same way.
Swinging is even more different, since it implies that the male also has (an)other partner(s) in return. Seeing his gf being fucked doesn't have to specifically excite him, even if it generally does.
You're right, it's not the same. In addition, there is also the fact that many words are used completely incorrectly here in the forum. Both NTR and cuckold were used when a partner, even if it was only an unrelated LI, also has sex with someone other than the MC. Which is so pasuchal but nonsense.
Nevertheless, swinging and cuckold are forms of sharing. Ssharing simply means that we share a permanent partner or a LI with others. Swinging is willingsly group sex, where it actually comes to partner swapping. As opposed to cuckold.
Cuckold once again assumes an existing relationship. In it's classic sharing-form the partner knows, mostly the man (but it can also be the other way around) knows that his partner has sex with others and agrees with that too. But he does not take an active part in the sexual part, but appears here voluntarily as a voyeur. He sits on the chair next to it and watches, is connected via webcam or telephone, or he is later told about the act in the form of photos or a story and gets excited about what he sees.
Next the cheating variant:
It's nealry the same. But here the voyeur doesn't consciously take on the role, but is forced into it. This is, for example, the classic revenge sex from the internet. A woman has caught her husband cheating, tricks him and ties him up. Then she has sex with someone else in front of his eyes. Or she's having an affair. Someone, maybe the lover, wants to hurt her husband, lets a camera run during sex and sends the video to her husband. And similar. This is actually about jealousy and humilation.
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Cuckold is usually considered NTR, as it is called netorase in the Far East. With us in the western world, however, this is often not regarded as an NTR, since we have the word cuckold for it. Therefore, games tagged with NTR are unlikely to include cuckold. In fact, we don't even have our own tag for it, so you have to be lucky and look for it, or look into all the games that are tagged with sharing, swinging or corruption. Unfortunately, this content is rare. I've looked at dozens of games for years, and I'm currently following several dozen with great interest. The real cuckold is nearly not present in any of them.
But I also admit that I'm not specifically looking for it. for me it's just a content like any other. Of course I'll take him with me if it happens to be in there.