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Mr. Big Bad may be the one who is directly responsible for the plot, but is not necessarily the most powerful or significant evil presence in the setting. the setting has a villainous presence that is more significant than Mr. Big Bad in the setting as a whole, but isn't causing the conflict of the story (and may have little to do with it at all). Perhaps it's an important being sealed or in eternal sleep.
Big Bad will seek to exploit or make use of it though this doesn't always happen. If the Big Bad tries to harness the Bigger Bad for his own gain, he'll likely learn the painful lesson that Evil Is Not to be Toyed with.
A Bigger Bad is a more threatening force of evil in the setting and overshadows it, but due to mindlessness, imprisonment, lack of interest, or other factors it is disconnected on a personal level from the main plot, which is caused by Mr. Big Bad. Contrast with Power Behind the Throne, where a villain directly tied into the story is revealed to be controlling or manipulating Mr. Big Bad. In this case, the Man behind the Man is the actual hidden Big Bad. A being who fits this trope is likely a demon lord, archdevil, God of Evil or Cosmic Abomination with an Evil Religion and/or Path of Inspiration built around him/her/it. He/she/it is probably Made of Evil and will probably exist As Long as There Is Evil.
He is one of a group of Cosmic Abominations or Mysterious beings who personify and provoke in humans various forms of madness.
He might a reincarnation of a Demon Lord.
In all cases he manages to be an even more powerful enemy, dangerous and deadly.
One of them is an entity that existed before everything and wants to plunge everything into nothingness.
Another is a life-hating Cosmic Abomination that turns every planet he visits into sand dunes.
Yet another is a monster born out of humanity's collective negative emotions.
They can also be a mad doctor who the aftermath of a devastating war, was sentenced to exile in Earth's orbit sealed within a space craft, who's body was modified into a cyborg contained within a bio-mechanical suit that would prevent him from deterioration and death. His memories were also converted into data, so that he would never forget his crimes, and was then banished into the wastelands he had created, to suffer eternally therein. Unfortunately, no one bargained on him coming back, and once he did, he set back to work.
They Might be the parent or creator the Big Bad
They can also be the reason why the Big Bad turned evil
In more mundane cases, this role can be taken by a distant dictator who is not involved in the plot or a cursed object but plans not only to enslave the world but the entire universe that we live in.
If you want an example used in a story I shall gladly give you one It would be a creature known as Chaos in the Japanese Cartoon Salior Moon
It emerges during the course of the series that Chaos sends out incarnations in the form of Sailor Moon's major enemies (for example the Negaforce), and eventually uses the last main villian Sailor Galaxia to steal people's souls so it can free itself and rule the galaxy.
That thing is is evil incarnate and the manifestation and the cause -of all of the sadness, cruelty, suffering and evilness in the galaxy
Chaos Existing solely to cause misery throughout the galaxy.
We barely even see what it looks like, and we never really see what that thing is....................Huh?
It is killed by Salior Moon but we never see it.
Where did that thing go? I hope it didn't survive that attack