From my well warped mind......
The Jag-Stang either had the same pickup marketed under 2 names or had 2 different pickups depending on production run stock from the factory.
The initial run (1995-2001) - Those guitars were marketed and said to have a DiMarzio pickup in them - which I can believe, as at that time of production, DiMarzio was Fender's primary pickup outsource (Fender always had an outsourced pickup brand, and then their own in-house designed and built stuff to provide a broader range of options - I think this started sometime in the eighties so they could built the Yngwie Malmsteen Stratocasters for production, which lead to Dimarzio pickups being used in a lot of guitars including the Heartfield series and Heartfield based Prodigy model). The initial Jag-Stang pickup was said to be a 7.71K Ohm Ceramic humbucker similar to a Dimarzio Evolution neck pickup called the H8 or Hsomething at least. They were notoriously bad and low output for the application these guitars would typically be used for. I have played one of these pickups in a 1998 CIJ Jag-Stang many many many years ago.
By the second run (2003-2006) - Fender had changed their outsource to Seymour Duncan (hence all the Duncan Designed pickups on Squiers, and the offering of the Seymour Duncan Pearly Gates in the LoneStar strat, among others). So Fender either used some Japanese made pickup possibly designed by Duncan, an approximation of the original H8, or something closer. I've had people tell me these newer pickups were better and hotter than the original Jag-Stang default bridge pickup. The pickup was marketed as the Fender "Santa Ana" Humbucker.
As for how it is now, I think Fender probably has some other arrangement now where they can use anyone's pickups, which would be the preferred thing as the mainstream technie guitar public wants glorious options from everywhere. I think it's way different now, that's the only way I could explain them having Seymour Duncan JB's in the Kurt Cobain Mustang and DiMarzios in the Jaguar. If it were 1993 and Fender was making those models, the Mustang would have a DiMarzio in it, and the Jaguar would be the only one doable 100%.