For the sake of good order, I would of course like to present the result of the sample order here:

It is difficult to reproduce the actual color in pictures, but the color variations are clearly visible here as well.
I ordered the roof tiles from Nelskamp as labeled in the pictures (note not all tiles are available in all colors).
- SIGMA-TILE (dark gray LONGLIFE matte)
- KRONEN-TILE (granite LONGLIFE matte)
- FINKENBERGER-TILE (black LONGLIFE matte)
- S-TILE (black LONGLIFE glossy)
Glossy is presumably not cost-neutral for us, but I still wanted to see the difference and have to say that I would not describe it as glossy. I had imagined black polished to be absolutely mirror-like intense, but in reality I think it’s safe to say: it’s just a little less matte than the others :D, so actually not really glossy. The color gradation between black and gray is very clearly visible in reality, black is really black and
not a very dark gray, which I like. The black "glossy" is a nice touch blacker than the matte, and if we actually decide on black (really black) windows, that will also be our first choice: the black glossy. You could also clearly see the difference when the tiles were wet from the rain; the glossy one is simply a touch blacker here as well.
By the way, the SIGMA tile has become our favorite, the S tile also appealed to us, although I can imagine that depending on the light incidence, due to the slight serration, a completely different roof is created. The SIGMA tile is simply uniform and rather round, it’s just more my style...