It doesn't stop at just the difference between SAE and Whitworth for imperial sizes. From 1/4" up to 1/2", SAE and Whit have the same TPI, only a different thread form (55 or 60 degrees). A nut from one can be put on the other but won't fit or perform at its best. At 1/2", Whit is 12 tpi and SAE, 13. Why is anybody's guess. For anything smaller than 1/4", there is no whitworth thread. Joseph Whitworth, the designer made none smaller than 1/4". Others have added ******* threads since and called them Whitworth but the intention was that for smaller than 1/4", the BA (British Association) system would be used. I think that is similar to the American system where they use 4,6 or 8 (for example) gauge screws (which are a mystery to me). I wonder if there is any correlation between those and BA
UNF is the fine thread version of SAE (UNC) and BSF, the British fine thread system (British Standard Fine).
As for the different sizes of the hex nuts and bolt heads, the Americans quote a simple measurement across the flats (AF) whereas, there is a formula in Whitworth to calculate the size of the hex and it is based on the diameter of he thread.
Then there is Metric! Oh so easy. I am nearly finished restoring a French car from 1928 and all of the threads are standard metric. That makes things sooooo easy. IMO, the best thing to have happened in the world of engineering is the (almost) universal adoption of the metric system. As far as I know, only one country in the world persists with the antiquated imperial weights and measures system and even then, it is not the imperial system that the rest of the world used to use. A real oddball!