JIC and AN are the same 37° flare, with the only basic difference being that JIC is usually brass or steel, and AN is usually aluminum (though Aeroquip, Earl's, etc. sell steel AN fittings, which are actually just plumbing-store parts). "AN" literally stands for "Army-Navy", which is where the JIC standard was applied to allow quick, reliable repairs and replacements in the field during battle. A little trivia: AN fittings as we know them first ended up on cars in the late '50s when enterprising drag racers were doing a lot of their shopping at army surplus stores. That trend continued for many years; the first modern Top Fuel supply pump, debuted at Indy in 1982, was actually something Don Prudhomme's crew chief found in such a store: a wing-tank fuel transfer pump from a B-52 Stratofortress.
SAE 45° in the JIC-style fitting is actually less common, though you will find it occasionally on cars and a little more often on diesels and medium/heavy-duty trucks. Generally, you'll see the standard used in an inverted-flare arrangment, such as brake and fuel lines. The non-inverted, JIC-looking fittings use the same threads as JIC/AN with the exception of -6 (3/8"), -10 (5/8") and -12 (3/4"), if memory serves (and it may not, so don't quote me). Mixed SAE/JIC fittings will not seal when used together. There is a specific type Parker fitting that will accept both, which has been a real trouble saver at the diesel shop. When playing at home, it's important to not mix the two because those Parker fittings are not parts-store items. There's really no reason to use non-inverted SAE fittings except on a factory application such as Torqueflite cooler line connections at the transmission. Other than that, in most cases you'll find SAE fittings in use on hydraulics systems; JIC is not common in that usage but it does exist.