Gravity vs Gravitational Waves

I thought I had a reasonable understanding of relativity, the speed of light speed limit, and how this stuff related to gravity. Then I read through all the answers/comments for this question:

How does Zumberge's 1981 gravitational measurements relate to gravitational waves?

And now I'm more confused than ever. Here's the opening for the (currently) most upvoted answer:

"This represents a major misunderstanding of what a gravitational wave is. The effect presented is simply the semi-static gravitational field at earth due to the earth, moon and sun. It is predicted by Newtonian gravity. There is no 'wave' that propagated, it's the instant positions of the 3 bodies that change over 1 day (and over 1 year also). "

So... my understanding of relativity prohibits the existence of a "static gravitational field" based on the "instant positions" of some masses. If it were allowed, that would imply that information about gravity traveled at infinite velocity which violates relativity. All changes in gravitational fields must propagate at a maximum of the speed of light.

Fundamentally though, I guess my big confusion is that it seems like everyone in that thread keeps arguing about some difference between "measuring gravity" and "measuring gravitational waves". Is measuring gravity equivalent to measuring magnetism around a permanent magnet? Is measuring gravitational waves equivalent to a digital camera capturing photons?

edit diving a little deeper

There's more context in the linked question, but I guess to begin with, I always assumed that "regular gravity" was "transmitted" via virtual particles of some type of gauge boson. So I always assumed that "gravity waves" then must refer to "real" particles in the same way that photons are real particles. Furthermore, afaik, there's no possible way to detect a static magnetic field using a mechanism which could also detect a photon. That's the whole point of a virtual photon.

So in terms of the magnet vs camera analogy, that doesn't make any sense to me in the context of the linked question. Let me bring some of that background here.

"This is the SAME gravitational wave effect measured by the LIGO researches recently

This is not a gravitational wave, this is a measurement of tides caused by the movement of a single detector within the earth-moon dimple. If there had been a second detector, it would have been clear that these tides do not propagate across the earth at the speed of light, but at the speed of the movement of the moon."

"LIGO actually detects, then filters out, this local gravitational wave

This uses the term "gravitational wave" incorrectly. It is more correct to say, "LIGO actually detects, then filters out, this local gravitational tidal noise."

According to the magnet/camera analogy, LIGO shouldn't even be able to detect tidal effects. It's fundamentally the wrong type of particle. Also, if gravity waves are the "real" equivalent of a force carrying particle, then there would be no need for a second detector. You don't need two cameras to take one picture... That doesn't even make sense.