3/8" x 24 TPI is a UNF (Unified Fine) thread tapping drill is 8.5mm
5/8" x 24 TPI does not exist in anything I can find the nearest UNF thread is 5/8" x 18 TPI tapping drill 14.5mm
(See Andrews reply below – 5/8" x 24 is probably UNEF – not a size I've come across before)
Threading a bar just start with nominal size so 3/8" dia and 5/8" dia.
3/8" an 5/8" BSW or BSF are much coarser than the TPI you have given. The nearest metric threads would be
10mm x 1 IsoMetric Fine and 16mm x 1mm IsoMetric Fine. Tapping 9.2mm and 15mm drill respectively.
If you are making both threads, internal and external unless there is a good reason ie matching existing kit just go for what you have or can easily get hold of. I would go for standard IsoMetric coarse as these are the easiest to get these days (unless you are in the States) but don't know if you can alter the bar sizes to suit?
John
Edit: Add ref to later post
Edited By Journeyman on 19/05/2021 09:28:43