They’re all the same thing! A Jinn is another term for a bootstrap paradox or causal loop. And 12 Monkeys is full of them.

Quoting from wikipedia:

A causal loop in the context of time travel or the causal structure of spacetime, is a sequence of events (actions, information, objects, people) in which an event is among the causes of another event, which in turn is among the causes of the first-mentioned event.

A 1992 paper by physicists Andrei Lossev and Igor Novikov* labeled such items without origin as Jinn, with the singular term Jinnee. This terminology was inspired by the Jinn of the Quran, which are described as leaving no trace when they disappear. Lossev and Novikov allowed the term “Jinn” to cover both objects and information with reflexive origin; they called the former “Jinn of the first kind”, and the latter “Jinn of the second kind”

* The full paper by Lossev and Novikov – The Jinn of the Time Machine: Nontrivial Self-Consistent Solutions (1992) can be read in full here

You can read more here: wikipedia.org/Causal_loop

and here : the-bootstrap-paradox-explained/

But that’s just the technical meaning.

Why did the show choose to use the term ‘Jinn’, rather than something that would be more familiar to sci-fi fans? We’ll have to wait and see, but it seems like it might have something to do with the almost  entity-like presence time has in the show.

We’ve heard the Jinn referred to three times by name leading into season 4. The first by Jones, the second by Cole (future asshole), and the last by the Tall Man in his sermon to the congregation of Titan, as he intones:

Like the Witness, we are all products of the Great Jinn!

So it seems The Jinn is not just something scientists talk about, but has become part of the 12 Monkeys’ cult mythology.