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Nominal pipe size is a label, not a measurement: 2 inch NPS pipe has a 60.3 mm outside diameter, not 50.8 mm. The outside diameter is fixed per size so that fittings interchange, and the schedule number sets the wall thickness, which eats into the bore. DN 50 is the metric designation for the same pipe.
Nominal versus actual
outside diameter is fixed per NPS; schedule sets wall thickness
Bore
inside diameter = outside diameter - 2 x wall thickness
The designation originally referred to the bore of thick-walled wrought iron pipe. As walls thinned the outside diameter was frozen so threads stayed compatible.
No, only the wall and therefore the bore. That is what allows the same fittings to serve every schedule at a given size.