Natural satellite == moon.

"Natural satellite" is a subset of "satellite", thus what you'd call them is correct by definition. Let's let the astronomers with credibility play and name the objects.

So does Saturn have billions of moons?

Saturn's rings are a bit more special. They are actually only 10-100m thick. There's still a difference (however small it may be) between those and kilometer sized rocks.

No need ti invoke Saturn, Jupiter has its own rings.

Do astronomers get as fiery about taxanomy as biologists do? I kind of had the impression they're easy going about naming, just more wary of upsetting young enthusiests. I heard there were many sternly worded letters from 9 year olds, after the demotion of Pluto.

Slightly related, are all the particles in (eg) Saturn's rings wver referred to as moons?

Seems like they do: https://arxiv.org/pdf/1805.04115.pdf

Oh wow. This is basically a paper about astrologists. Was it published under astrology or anthropology?

I agree, however with so many "moons" now known and more being discovered constantly, and so many of those being really nothing more than asteroids and possibly fragments and debris from past collisions, and in light of the change of the definition of "planet", I would not at all be surprised if the astronomers decided to change the definition of "moon" to also include hydrostatic equilibrium, and then captured asteroids like Mars' to be renamed "minor moons" or similar.

From the above article:

So as it stands, a moon is simply any natural body in orbit around a planet or other non-stellar object (so asteroids can have moons, and it’s even possible for a moon to have its own moon, although none have been discovered so far).

Behemoth ISS is 0.0728 kM across.

But moon anyway mostly just means natural satellite.

Instead of moons, maybe they're space stations?