...and a field is just a value that behaves in a particular way. An example outside QFT: phonons [1] behave like particles, but there is no "palpable" sound field, there's only local distribution of implulses of the molecules of air (or whatever medium) where the sound propagates.
Other fields can be seen as attributes of the space itself, and "elementary particles" as wrinkles on it. Gravity is special because it bends the very geometry of space.
> Gravity is special because it bends the very geometry of space.
It's important to remember that this is not true in QFT, and QFT is not true in GR. That is, the math of QFT does not work if spacetime can become curved (at least, if it can become significantly curved).
Maybe you want to leaf through a copy of Birrell & Davies or Parker & Toms again. QFTCS is good in strong gravity, and is as good as anything else at transplanckian scale (which is to say there's presently no way of knowing when around there QFTCS becomes a bad approximation to an unknown quantum gravity).
We should also remember the enormous cosmological curvature in which testable quantum systems exist; it's not just about compact objects. Significant? There's observed H-sources above z ~ 15, and of course the CMB photons at z ~ 1100. Indeed, B&D deals with Robertson-Walker spacetimes over several chapters before they get to black holes.
Also at the weak but measurable curvature regime there's e.g. Pound-Rebka, time metrology[1], and so forth, and lots of spacecraft confirming the strong equivalence principle (e.g. MESSENGER, LAGEOS) and thus supporting the LLI one expects to find in relativistic QFTs of the sort one would use to describe the behaviour of laser altimeters, distant astrophysical masers (and the Lyman-alpha forest), the spectral lines in stellar atmospheres and so on.
Every particle type has its own field, but the OP article is counting a single particle type multiple times based on properties like spin and polarization. At one point the article reaches the number 118. That corresponds directly to 37 quantum fields once you take the "double counting" into account.
No, that's just the vacuum state of any of the standard quantum fields.
"Field" is being used there in its general sense, of a quantity that has a value for every point in space and time. It's saying that in a (region of a) quantum field that contains no activity, there are nevertheless random fluctuations, which can themselves be modeled as a field. But they're not separate from the quantum field that gives rise to them - they have all the same fundamental properties.
37 is what you get from counting Dirac matter fields (24) plus gauge fields (12) plus the Higgs. That's post-symmetry-breaking, and doesn't account for chirality.
If you count fundamental field components in the electroweak-symmetric Lagrangian, you get 43. I broke down both of those numbers in my comment linked above.
> If you pick and choose which properties to select as unique fields, maybe you can get the number 37, but at that point why not 118 fields?
There's no picking and choosing involved - quite the opposite. It's counting what the QFT math specifies. Particles with e.g. different color charges can't share the same field. To get to 17 from either of the above, you have to ignore quark color charges and the different gluon types. It's essentially a classification of types of particles that combines field together, it's not a count of fields.
Other fields can be seen as attributes of the space itself, and "elementary particles" as wrinkles on it. Gravity is special because it bends the very geometry of space.
[1]: https://en.wikipedia.org/wiki/Phonon