Villain for a Villain is a common theme founded within media and books in general, and it is usually when a villain (Usually a Big Bads and ocasionally neutral characters) have his owns demons or principals instigators, but in this case, this characters are truly evil, and more despicable and disturbing than the former.
Who are they and what made them different from a Designated Villain or other Threat
To clarify, A designated villain is usually heroic, anti-heroic or good character who only is doing his job, but is always antagonized by the villain in question, A Villain for a Villain, is the exact opposite of that and they are usually and commonly are truly evil, at first they appear as friend or "affable" character who to the villain (and some times a hero) in question, but at the end they ditch and reveal his true nature when the villain in question transformed in something worse than her previous self.
A Villain for a Villain commonly is The Heavy in the story, because they make others villains in his own image, They always appear as "friendly" old man, A little boy, or some random mysterious but nicely objects, Others of this kind of character appears as outright evil force who corrupt a evil character in a Complete Monters, Others them try to kill the villain in question to eliminate "The Competence", or they no need his service anymore (You Lived Your Use Usefulness).
Although, but it is not the case, they can appear when there are Villain protagonist in his story, they can tale about who made them the monsters they are in first place.
This always lead to a final encounter, with the former villain (or villains, usually they create more than one) and heroes put them a side his difference to defeat them (Similar to an Evil Vs. Evil Scenario), and won, but this sometimes only give to them a short lived period of peace until they return, John Milton is a good example of this.
- Morgoth (Middle-earth) - He is, without a doubt, a good example of this. He was the former Vala of Eru Ilúvatar, who not only corrupted many Maiar in his quest for power, he was, in fact, the true master of Sauron, who was corrupted to continue his quest of destruction. At the end, Morgoth was bound to great chain Angainor, but this resulted in a prophecized return.
- John Milton (The Devil's Advocate) - Another good example of this, He was presented as a charismatic who give them to Kevin Lomax more cases just to grow his ego and the end, this result revealing his true nature as Satan and try to tempt his son to make with his half sister the anti-christ, however kevin commited suicide and a new circle of life to kevin, but this result in Milton to try again corrupt kevin once more.
- Prince Hans (Frozen) - While Technically this a "Kid-Friendly" version, Prince Hans is another good example, always using his charm and charisma to woos princess anna and queen elsa, to just at the end revealing his true nature as a liar, and usurper who wants the Kingdom of Arendelle just to himself.
- Eddy's Brother (Ed, Edd n Eddy) - Eddy's Brother is perfect example of this, at first he appears to Eddy a protective brother, just at the end revealing his true nature as sadistic man who think little to no about his little brother, and Worse make eddy his greedy personality and he make all the kisd of the cul-de-sac to hate him, at the end this proved to him to be his great failure.