If you look up "cambion," you will most likely find sources telling you that this word refers to the offspring of a human and a demon - more specifically a succubus or incubus. But that's not what the word used to mean. Cambion comes from the Latin cambiare, to change. A cambion was originally a changeling.
This confusion isn't new. There are essentially two similar traditions of the Demon Baby, which have always been very close and prone to mixing up.
Today, cambions would be defined as Type 2. But when the 13th century bishop William of Auvergne mentioned cambiones in his work De Universo, he was describing Type 1.
"You should not overlook what is said about infants whom the convention calls cambiones, about which the most widespread are old wives’ tales: that they are the children of demon incubi, substituted by female demons so that they are fed by them as if they are their own and are hence called cambiones, that is, cambici, as if swapped and substituted to female parents for their own children. They say that these are thin, always wailing, drinking so much milk that it takes four wet-nurses to feed one. They are seen to stay with their wet-nurses for many years, after which they ﬂy away, or rather vanish." (Translation via Stainton and Goodey)
William's "cambiones" are the offspring of incubi instead of fairies, but otherwise, they are the same. They eat, they scream, and they plague the families whose children they have replaced. In fact, Richard Firth Green remarks that "incubus" was “probably the most widely used general scholastic term for ‘fairy’ in the Middle Ages." (p. 3) William's account is one of the earliest full description of changelings.
The common people would not actually have called them cambiones - that's Latin, so I'm not sure why William of Auvergne says it's a word of the "vulgar" or common tongue. Richard Firth Green in Elf Queens and Holy Friars: Fairy Beliefs and the Medieval Church has a detailed study of changelings in medieval belief. He gives a list of contemporary French and English names for this kind of creature: chamion, conjeoun or cangun. The word changeling did not show up until fairly late. The Oxford English Dictionary found it first in print around 1534.
In 1487, the Malleus Maleficarum appeared on the scene. This was "The Hammer of Witches," a medieval book still infamous today. It was all about witchcraft and what people should do about it (spoiler: burn all the witches).
It touched on the subject of demon-human hybrids a couple of times, but the part relevant to this discussion is Part 2, Chapter 8.
"Another terrible thing which God permits to happen to men is when their own children are taken away from women, and strange children are put in their place by devils. And these children, which are commonly called changelings [campsores], or in the German tongue Wechselkinder, are of three kinds. For some are always ailing and crying, and yet the milk of four women is not enough to satisfy them. Some are generated by the operation of Incubus devils, of whom, however, they are not the sons, but of that man from whom the devil has received the semen as a Succubus, or whose semen he has collected from some nocturnal pollution in sleep. For these children are sometimes, by Divine permission, substituted for the real children.
And there is a third kind, when the devils at times appear in the form of young children and attach themselves to the nurses. But all three kinds have this in common, that though they are very heavy, they are always ailing and do not grow, and cannot receive enough milk to satisfy them, and are often reported to have vanished away."
This, and Martin Luther's "Table Talks" published in 1566, would become the most widely cited authorities on changelings (or in German: Kielkropf, Wechselkinder, or Wechselbälge). Luther's version would fit both Type 1 and Type 2, as they were the demonic children of Satan and human women, whom Satan then swapped for normal children. As Luther said,
"This devil will suck and eat like an animal, but it will not grow. Thus it is said that changelings and killcrops do not live longer than eighteen or nineteen years."
Less than a century later, Pierre de Lancre was a French judge and performer of a huge witch hunt. Among his books on witchcraft was Tableau de l'inconstance des mauvais anges et démons (1612). (Read it in English or French.) Like many of his contemporaries, he touches on the question of whether demons could procreate. He mentions cambions and, in describing them, cites Martin Luther and says that their "age is fixed at seven years." Despite specifically calling these children "changed children" (enfans Changes), he also seems pretty firm on the idea that these are "children born from sexual union with demons." Finally, he cites a story from the encyclopedic Dierum canicularum (Dog Days) by Simonis Majoli, which was printed in 1597. Although I have not been able to track down this tome, the story as de Lancre gives it runs like this. There was a beggar who always carried a little boy with him. The little boy never did anything but scream and cry. A horseman saw them trying to cross the river, and helpfully took the child onto his own horse, but the boy was so heavy that the horse nearly sank. The beggar later confessed that the boy was actually a demon with whom he had made a deal. As long as the beggar carried him around, everyone would give him alms.
Later scholars would give this story significantly different spins, forget that it was Majoli or de Lancre who told it, and misspell de Lancre's name.
The Dictionnaire Infernal by Jacques Auguste Simon Collin de Plancy, first published in 1818, includes the cambion but is rather misleading. It cites Delancre as saying that incubi and succubi produce children called cambions. This can imply that the cambions are born of incubi and succubi together, rather than an incubus-human or succubus-human relationship. The author repeats that Martin Luther said changelings lived seven years. This is clearly wrong, since Martin Luther talked about changelings living until eighteen or nineteen. De Plancy also includes the story of the beggar, but attributes it to Henri Boguet's Discours de Sorciers. (I cannot find the beggar's tale in that book at all, leading me to wonder if De Plancy misread De Lancre's citations.)
The Dictionnaire's influence is seen as soon as 1861, when Dudley Costello published Holidays with Hobgoblins: And Talk of Strange Things. When he includes the beggar's tale, he describes the baby explicitly as a Cambion and the child of an incubus and succubus. Remember that de Lancre called it only a demon.
Lewis Spence's Encyclopædia of Occultism (1920) also relied on the Dictionnaire Infernal. He defined cambions as "offspring of the incubi and succubi," citing Delamare. (Whoops.) All of the information is pretty much just a translation of the Dictionnaire.
This new definition spread into popular culture. In Toilers of the Sea by Victor Hugo (1874), the main character is rumored to be a cambion, the son of a woman and the devil. One poem entitled "Cambion" in Clark Ashton Smith's The Dark Chateau (1951) runs "I am that spawn of witch and demon." Dungeons and Dragons brought out its Monster Manual II in 1983, with the demon-human-hybrid cambion.
The evolution of the word is pretty clear, with both meanings having always twined around each other. There was overlap between fairies and demons as the Church demonized older traditions. The half-demon man was a common trope in medieval lore, like (again) Merlin or Robert the Devil or Sir Gowther. Some version of "cambion" was once an insult common to "bastard." There are other words out there for the same idea. For instance, Jakob Grimm's Teutonic Mythology vol. II (1844) says that the children of witches and devils are elves, Holds, or Holdiken.
However, it's sobering to remember that many of these stories originated in trying to explain children born with congenital disorders. For instance, a severely disabled child whom Martin Luther saw and believed must be a demonic being deserving of death.
Researching folktales and fairies, with a focus on common tale types.