https://typpo.github.io/spacekit/examples/saturn/index.html
Besides the 20 new moons, I find it interesting that there are 8 "lost" moons. These are objects observed as far back as 2004 - but their current locations are unknown.
Sorry but this is the end of my comment.
Polar orbits are "unstable" in a few senses, namely that even in an ideal setting orbital planes will precess around central masses that are lumpy rather than spherically symmetric; rotation of a lumpy central mass introduces further precessions. Nodal precession is pretty interesting, for example. One can concoct all sorts of odd orbital changes by perturbing the rotating central mass "under" a test object in stable orbit.
However, in the case of known solar system bodies, slowly shifting a satellite in near-polar orbit into a near-equatorial orbit conflicts with quite a lot of evidence; by the mid 1960s it was pretty safe to say that known inner moons maintain over very long timescales an almost constant orbital inclination with respect to the planet's equator, while outer moons maintain an almost constant orbital inclination with respect to the invariable plane of the solar system. Interesting exceptions are Triton and Earth's moon, both of which have significant inclinations to their planets. Precessions are primarily driven by the planet for the inner moons, and by the sun for the outer moons.
It's probably worth paying some close attention to Uranus and its known moons (and their formation and/or capture) when considering the various thoughts people have put into the thread. Most of the moons and rings have negligible inclination (i.e., they're coplanar with Uranus's equator), and Uranus's extreme axial tilt is intriguing. If the tilt is because of a giant collision, did the relevant moons and rings follow the planetary tilt? Or did they form in the highly-tilted equatorial plane (for some of the moons), or were they captured into the equatorial plane (for others) post-tilt?
All of the discovered retrograde orbiting moons are in similar orbits which suggests they all came from some larger object broken apart. Keep in mind all of these new objects are quite small, just a few miles across. About a billion of them could fit inside Saturn's largest moon, Titan (seventeen were discovered).
Regular moon fits with what I was talking about before.
Irregular moons are the ones with eccentric, retrograde, or otherwise weird orbits and acquisition histories.
The more you get into specifics about this kind of thing, the less concise and accurate you can be, it would take an expert up to date with the literature to go much deeper.
With planets, we started getting too many "planets" when we discovered more and more really tiny ones, so we started coming up with new names for them: "dwarf planet", "Trojan", "asteroid", etc. A small rock in the asteroid belt orbits the Sun, but it still isn't called a "planet".
It sounds like we need to do something similar with moons, or else it's going to get out of control. There's likely an absurd number of small rocks orbiting Saturn and Jupiter; should they really all be called "moons"?
Well, some of them are called "rings"...
There are short Wikipedia articles for each one.
JPL provides orbital elements but presumably they are not quite correct, otherwise we could locate them: https://ssd.jpl.nasa.gov/?sat_elem