broadly speaking there are two categories, technical LUTs and creative LUTs. I would probably call all the examples you looked at creative LUTs, just because they haven’t necessarily been made with the same rigour as a print film emulation (PFE) LUT from the film industry.
which leads us to technical LUTs, of which there are kind of two main categories as well, LUTs that go at the beginning of the image pipe and LUTs that are the final step in the pipe.
the PFE LUT is an example of the latter, they came about in the early days of digital intermediates, where movies were captured on film, scanned digitally for editing, VFX, colour work, etc, then printed back to film for distribution. So as we know, film will always have some effect on the colours and contrast of whatever’s being captured, and the role of the PFE is to accurately represent this transform. The colourist can apply the LUT in their final node, adjust the image seeing what it will look like once its printed to film, then can turn it off before they send it off to be printed.
now with digtal distribution it has evolved into more of an artistic tool. Digital projection doesn’t impart the same sort colouration, so in some cases people will still use a PFE LUT and just leave it on. In this case of course there are no rules as its only serving as a look, so you can use the PFE LUT earlier in the pipe if you want.
the other LUTs that go up front are typically for transorming large gamut colourspaces with log gamma (cineon was the classic curve for digitizing film, and most digital camera manufacturers have their own) into a Rec709 or Rec2020 colour space to make sure all your values are legal while preserving colours accurately.
then most of the LUTs leftover are creative LUTs, and in most cases there’s no telling what they’re trying to do, with at least one notable exception: often a director, cinematographer and colourist will try to develop the look of a production quite early on, and using test footage they will create the look they’re going for and use that as a monitor LUT on set. Because you’re likely shooting log or RAW, and will need a standard conversion LUT to get a more legiable image anyway, the idea is to replace this with a viewing LUT to give you a better impression of the final look you’re going for. Sometimes people will even bake in exposure compensation and things like that as well.