Nicely described. May I add:
This happens with any other process that transforms the raw milk protein caseinogen into casein, the main protein of cheese, or simply precipitates it out of solution in the milk. Acidifying the milk can do it, or treating it with rennet. The first product of rennet is a beautifully smooth mass called junket, a product my mother loved, but which I found nauseatingly bland. Junket displayed the effects described with yoghurt even more strongly.
Suitably treated, that casein mass forms curds, and with most of the whey squeezed out of them, the curds are the first stage in the process of making cheese.
Note that little Miss Muffet was eating her "curds and whey"; it seems that she was fond of junket too, and that is just about what one would expect from such an insipid little misarachnist!
Go well,
Jon