A half-inch BSP nut is much bigger than half an inch, because it fits on the outside of an iron half-inch bore pipe, after it has been threaded.
On the other hand, 20mm plastic pipe is (about) half an inch internal diameter., and 15mm copper is, too. So is half-inch copper pipe, which you will find in old houses (it's near enough 15mm o.d. that you can use the same olives and compression fittings)
AFAIK Imperial sizes of pipe are always quoted by their internal diameter, and Metric sizes by their external diameter.
if you are very old you will have used pre-AF spanners in sizes that seem to have nothing to do with the size stamped on them. This is a source of great entertainment. Americans still have problems with nut, bolt and drill sizes.
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