Glad you got sorted in the end. As you discovered 7/16 BSW and 5/8 BSF are indeed exactly the same thread. Just different diameters.
Pipe threads are the classic ones for catching normal mortals out as they are specified by the size of the hole in the pipe not by the outside diameter like (nearly) everything else. Fortunately the other oddities are seriously obscure.
BA is the other one that can drive you nuts as they are a metric dimensioned thread specified in imperial units. Which reminds me. 0 BA will screw into 1/4 BSF and 2 BA into M5 and merely feel slack. Be careful not to do this as the joint will be extremely weak and probably not stay done up.
Here is a link to a really useful tabular Compilation of Thread Size Data originally created by Andy Pugh.
https://fromtheframeup.com/uploads/T...size_chart.pdf
As the list is sorted by bolt (or stud) diameter its an excellent resource for figuring out what size any particular fastener is. Conventional listings are by type then size so first you have to figure out (guess) which breed it is.
Nuts are possibly more of a problem for normal folk. Best way for normal folk is probably to screw the suspicious object onto a bolt. Alternatively measuring the size of the nut, an open ended spanner will do just fine, will rapidly narrow the list of possible suspects. Out in the normal world there aren't really that many combinations to worry about.
Its not a bad idea to invest in a test box containing one labeled sample of each size you expect to encounter. Something I have been threatening to do for at least 50 years! Best paint them pink so you aren't tempted to dip into the box to replace one that has gine walkabout.
Clive
PS If anyone is wondering that list is, from a wider engineering viewpoint, by no means comprehensive.