The difference is not between JIC and AN. the difference is between JIC / AN and SAE which is mostly common brass fittings.
Most sizes except no6 (different size) and no12 (different thread) will "screw together" between JIC/ AN and the SAE
The difference is that SAE have a 45 degree flare angle, and AN/ JIC has a 37 1/2 degree flare angle.
IN SOME CASES you can interchange them, but you may have sealing problems. Also, interchanging fittings might damage one or both fittings, so that "next time" if you screw one fitting into it's proper mate, you will still have sealing problems as one is now damaged from the improper flare angle.
(Say you have a hydraulic hose on a tractor, log skidder, etc, and the parts place makes you a new one, but they put no8 SAE ends on instead of the no8 JIC which came off. You put the hose on, tighten the 'ell out of it, and it works. Maybe NEXT time that hose blows, you end up with the proper JIC. But now the mating adapter has been damaged, and the thing LEAKS)
GENERALLY brass is SAE
Steel or alloy is generally JIC / AN
On the older cars, anything flare such as transmission coolers would have been SAE regardless that it is steel. Some power steering (might be proprieatary) if it's flare, will be SAE
Older commercial refrigeration fittings would have been all SAE
If you hold a 37 and a 45 degree male flare side by side you can easily see the difference
(The trick by the way is getting a sales person who actually knows fittings. I went into O'Reallys the other day wanting "Two 5/16 SAE flare caps" and I could tell by the stare-into-space look that he had no idea. Even when back at the Weatherhead/ Imperial / Edelman brass cabinet, he was no help. HERE's the THING about automotive/ hardware store brass................ The common brand name brass cabinets are all COLOR CODED!!! "All the green drawers" are SAE)
And by the way nearly none of the auto stores will have any AN/ JIC unless they stock some "speed shop" stuff or make hydraulic hoses.