Having dealt with 18th c. screws, maybe I can answer part of this.

There were tool companies making tap & die sets ( or sometimes, taps and screw plates) and they would come as a set, and vary somewhat from company to company. So, if you were a blacksmith, and had a screwplate & taps from John Wyke, it would match other John Wyke screwplates, but maybe not somebody else's. Not long into the 19th century industrial revolution in England , there's a system: the Timmins & Sons tool company was listing screwplate sets with standard sizes of #6, 7, 8 or 1/2", 5/6", etc. by 1845, possibly as early as 1820's. Joseph Clement was pushing for standard sizes by 1828, and likely some of it was also due to the invention of the screw-cutting lathe by Maudslay. I also think the clockmakers in England may have standardized among themselves earlier, especially in Lancashire- but I am not sure.

I am not sure when Metric sizes were standardized, and I really can't speak as to when ( or, really, why) the British Standard and Whitworth thread systems were created, which is kind of between the English and Metric. Now, as far as making screws fit: there is a certain amount of play - even in the Timmins catalog, you could get "full" or "bare" screwplate sets, to make tighter or looser screws, and modern dies can be adjusted to make bigger or smaller screws, as well. How much play can also be specified- if you look in any edition of machinery's handbook, you'll find the specs.