In simple terms, the biggest difference in form is the included angle on the various threads, with the 'whitworth' angle - for all BSW and BSF - being 55°.
BSC is 60°, so are UNC and UNF, and most if not all metric, while BA is 47.5°.
There are differences in roots and crests and stuff which the long read referenced and other similarly scholarly sites explain in horrible detail, along with the important stuff like 'how many threads to the inch' (or millimetre equivalent) for a given size.
Some series overlap on the pitch/threads per inch, like M6 and 0BA at 1mm, or 1/4 Cycle and BSF at 26 tpi, and a few UNC and BSW sizes share their tpi.
But for a '50s beesa it's going to be mostly BSC, a bit of BSF, some BA for the electrical side and maybe (trying to think of something) BSW. Except where POs have decided on something else . . . which they often might have. Plumbing sizes for fuel taps and unions - BSP (whose sizings are done on the bore of what is to be screwed into them, so they sound far smaller than they are).
I'm with Terryg - Tracy Tools for the basics and add when required. Decent enough quality, fair prices, rapid service, I have always found, and a huge range.