I wanted to say Catherine II 5 kopek, but apparently the "cartwheel" twopence from 1797 is a bit thicker. (That's one of the coin types in my long-term wish list... they circulated so little that worn examples are very hard to find, and high-grade examples are orders of magnitude beyond my budget!)
However, the 5 kopek coins varied a lot in weight (the standard is 51 grams, sure, but apparently actual weights were all over the place from 30 to 80 grams). Since the diameter was fairly well standartized, the difference must have been mostly in thickness, which means that the heavier examples should be thicker than the 1797 twopence (not mine - my two examples appear to be 4.3-4.8 mm; hard to say more precisely because the high-relief design gets in the way).
As for thinnest, you should look for medieval bracteates - coins so thin that they could only have a design on one side, and the other side was its mirror image. Supposedly some Norwegian examples only weighed 0.1 grams - they must have been extremely thin!
I don't have any of those, unfortunately. I do have a uniface Salzburg pfennig from 1521 that shows part of the mirrored design on the blank side; I measured it with my caliper, and got 0.45 mm. Which is thicker than I expected, actually.
(Incidentally, anyone knows what's the thickness of early Roman Republican copper as and semis coins? Something like
this one? They should be well in the running for thickest, being silly heavy.)