I would like to propose a different theory, which I think is much simpler, and consistent to what we know about the wizard society. Maybe half giants are a rare type of giant who, quite ironically, suffer from the giant equivalent of dwarfism, and the notion that they must be the offspring of humans and giants is just a myth or misconception. People in the wizarding world seem to be very poorly informed about other magical species, and that led some of them to actually believe this. As half giants are so extremely scarce, it is hard to dispute this idea.
Meanwhile, giants are very proud of their size and strength, so, upon seeing how children with this uncommon condition would be outcasts in the community, probably killed or left to die, there were a couple of times when the occasional wizard envoy/researcher among them would end up adopting said children, who were not only smaller, but more prone to use magic.
Hagrid is very sweet and somewhat simpleminded, and it would be easy to convince him that a man could fall in love with a giantess, since he himself loves unusual creatures, in his own nonromantic way. Maybe his father was only “broken-hearted” to remember how a giantess abandoned her child, and would never tell him the truth. It is possible that when Hagrid was still a baby, he grew attached to the human, the only one around that would care for him, and never doubted that he was his father.
Madame Maxime, on the other hand, is much more intelligent and sophisticated. Well-informed people like her know that "half" is just a reference to their height (the same way Tyrion from Game of Thrones is sometimes called the Halfman), not their bloodlines. She is aware of why she is what she is, and struggled to try to pass as human because she does not want to be erroneously seem as “half” a person, neither is she willing to admit that, among giants, she is an undesirable figure. It simply has a different connotation to her, because, after all, she was not as naïve and spared the implications of her condition as Hagrid.