The roots of the pipe schedule problem go back to the 1880's
It was intended that ASME would drop the schedule designations in the 1940s, but some people still persist in trying to use them.
You should not.
Call out your pipe using Outside diameter, wall thickness and weight per unit length.
4000 FT, PIPE, 12.75" OD x 0.500 WT @ 65.42 lbs/ft, ASTM A106-B
Schedule 80 S=>for Stainless Steel) is 0.500" (12.7 mm) wall thickness.
Carbon Steel Pipe Schedule 80 is 0.750" wall thickness.
See ASTM A358 for larger sizes of stainless pipe.
If it ain't broke, don't fix it. If it's not safe ... make it that way.