Q. Is cuckolding the same as swinging or having an open marriage?

Often people confuse cuckolding with swinging or polyamory, but cuckold is different in that the husband is loved by his wife only. He allows her to experience pleasure with another man. But, he does not want her to fall in love with the other men, only just receive pleasure from them.

Q. A cuckold marriage ... what exactly is it?

I describe cuckolding as a marriage where the husband derives sexual pleasure from watching his wife have sex with a man who has a larger penis. 

The couple forms an agreement in their marriage allowing the act of cuckold, which can vary in degree from role play for some couples to an lifestyle of actual cuckolding (the wife engages with sex with other men in front of her husband). This knowledge and tolerance of the wife's activities with other men makes the husband in such relationships a whimp/ sissy  properly speaking.