I’ll try to keep it simple: Basically, pickups are magnets + wire. The wire is wound around the magnet(s) in a coil.
A single coil pickup is just that: a single coil of wire around either magnetic rods (Fender) or steel screws that connect to a bar magnet (Gibson).
Vintage Fenders have single coil pickups that are all wound the same way: the magnets are aligned in the same direction, and the coil is wound in the same direction. All early pickups were made that way.
Then Seth Lover at Gibson figured out that if you put two coils together and reversed the magnetic polarity and the direction of the wire coil on one of them, you got a pickup that didn’t hum. The shorthand version of that is RW/RP: Reverse Wind, Reverse Polarity.
Meanwhile, back at Fender, they stuck with single coils. Most Fenders have two s/c pups, the Strat has 3. Vintage Fender wiring has all pickups wired in parallel.
At some point in the 80s (I think) Fender decided to change that and nowadays many Fenders have one pickup RW/RP to the other(s). Middle position (both pups on) on the Tele, Jag, Jazzmaster, etc, and positions 2 and 4 on a Strat. That means that those positions are now humbucking. They’re still wired in parallel, which means they sound like two single coils, not one humbucker, but the hum is bucked.
It is possible to wire a Fender-type guitar so that you can switch between parallel and series, which means that, in series, positions 2 and 4 on a Strat sound more like one humbucker than two single coils. Not exactly the same, but closer.
It’s also possible to switch between series and parallel in a humbucker. That’s also a useful sound, a humbucker in parallel is lower in volume and has less of a midrange spike. To my ears, that’s a much more useful option than splitting (or, as it’s usually and incorrectly called, “tapping”) a humbucker. Half a humbucker does not sound like a good single coil pickup, it sounds like ass in my opinion. But a humbucker in parallel sounds less “humbuckery” and more “single-coily” and has the extra benefit of still not humming.
On most Gibson-type guitars, the two humbuckers are in series within themselves but in parallel with each other. That can also be modded.
The reason why genuine out-of-phase options are rare is that it sounds like ass. Thin and “plinky”. There are a few people who like that sound and find it useful, but most players find it useless. Two humbuckers out of phase can sound OK because humbuckers are usually fat and loud enough to compensate a bit. Two Fender-type single coil pups out of phase is a very thin sound with a big drop in volume compared to the normal in-phase sound that some people (very incorrectly) call “out-of-phase”.
Two single coils in series but out-of-phase is a little more useful because series wiring gives a bit of a volume boost, but it’s still pretty bad sounding. I’m not just repeating things I’ve read here, by the way, I’ve experimented with all this stuff myself.
Hopefully that should give you a better understanding of how pickups are wired and what the various wiring options can do.