The definition of cuckold is (3 different sources):
"a man whose wife is sexually unfaithful"
"The husband of an adulteress"
"If a man is cuckolded, his wife has a sexual relationship with another man."
Applying the definition, a husband whose wife cheats is a cuckold. Knowing, approving, frequency, humiliation, swinging have absolutely nothing to do with cuckold. It's binary, if she had sex with another man. he's a cuckold!
The definition of hotwife is (3 different sources):
"A married woman who is allowed and/or encouraged by her husband to pursue sexual relationships with other individuals."
"A hotwife is a married woman who has sexual relationships outside of her marriage, with the full knowledge and consent of her husband, who himself doesn’t have affairs."
"a wife who has sex with men other than her husband, with the husband's approval."
Applying the definition, a wife who cheats is doing so behind her husbands back therefore the husband's knowledge is missing. Again binary, he is unaware therefore she is NOT a hotwife.
The definition of cheating:
"to secretly have sex with someone other than your husband, wife, or partner." MacMillan Dictionary
"to be sexually unfaithful —usually used with on " Miriam Webster
"If you cheat on your husband, wife, or usual sexual partner, you secretly have a sexual relationship with someone else" Cambridge
Hence cheating doesn't make the husband a cuckold nor does not cheating. Again cuckold is binary if a wife has sex with somelse the husband is a cuckold. REGARDLESS OF LIFESTYLE CHOICES!!! Full stop.