Right, that's exactly why I originally stated that you can always, in principle, distinguish between lab-grown and natural stones - it's just a matter of how hard you look, with what precision, and with how many analytical techniques. Therefore, the claim that "synthetic stones are identical to natural counterparts in chemical composition" is a moot point - I guarantee that, eventually, I will be able to find a difference in trace elements, isotopes, etc.
We stray far from the original topic here, and it doesn't really matter, as long as we know what someone is frying to say when they say "synthetic" or "simulant" - but my point is that one shouldn't have strong opinion, as synthetics will never be truly "indistinguishable" from the natural material.
We can find all sorts of differences in the same types of various natural stones. Diamonds can have different crystal structures different impurities, and can even have vacancies in the crystal lattice. Beryls, calcite and various other stones can have various crystal structures. I have found various forms of gypsum as selenite, satin spar, and alabaster in numerous different crystal structures and in various colors (white, red, blue, green, golden, tan, dark brown). And not all stones have crystal structure. There are around 300 types of opal, most of which are completely amorphous. Therefore, crystal structure is pretty much irrelevant. Although, Len Cram I mentioned earlier is producing precious opal that cannot be distinguished from naturally occurring opal.
Opal can also vary a lot in chemistry. Even though all opal contains amorphous silicon dioxide and water, it can also contain a lot of other things. These include crystalline silica, aluminum oxide, uranium, cinnabar, sodium, potassium, carbon, lithium, cobalt, thorium, iron, magnesium, barium, titanium, vanadium, copper, manganese, zinc, nickel, etc.
So getting back to my original point, a synthetic is not based on impurities or crystal structure. A synthetic is a stone that has the same chemistry and form as the base stone. As where a simulant is not the same as an synthetic. A simulant is a substance that has the appearance of the real thing, but without the same chemistry. Therefore, your claim of "eventually, you will find a difference, no matter how small, between the synthetic and the natural material, and thus the "synthetic" will suddenly become the "simulant". There is no objective distinction between the two categories," is incorrect. If we go by your definition then we would have to conclude that amethyst and citrine are quartz simulants since they differ compared to a natural pure quartz crystal.