These fittings are something of a bastard child. The only thing that these 7/16in. x 19tpi fittings really have to do with the BSP series is the 19tpi. pitch and that their function is to hold bits of tubing together! It is easy enough then to see why they all get lumped under the general heading of “plumbing”!
The 19tpi pitch, (1/4 & 3/8 BSP), is as far as I am aware unique to the BSP series. Certainly the 7/16in. O.D. has nothing to do with BSP based as it is on the bore of the pipe plus the wall thickness and thus none of the threads in the BSP family finish up with nice round numbers.
The real difference between BSP and these fittings is that the thread is not made on the pipe but on the parts fitted to the pipe. That shift coupled with thin walled solid drawn tube permits of much lighter section parts and that in turn requires different threads.
My guess is that what we have is an historical adaptation; companies making iron fittings would have had tooling to hand so when they branched out into the lighter, mostly nonferrous fittings, they made use of what they had. After all if you have a capstan set up for 19tpi threads why change it?
And if you have a spare moment over Christmas ponder on this: Small stuff is called tube, big stuff is called pipe. So then the question is at what point does a tube become a pipe?
If small stuff is called a tube why do we refer to petrol and oil pipes?
‘Appy Christmas all!