Steels are
routinely classified as high carbon alloys, low carbon alloys

I'd disagree with that, Dave. Alloy steel usually means steel containing
chromium or other elements to increase corrosion resistance, strength, creep
resistance, etc. People talk of high carbon steels, which are hardenable and
difficult to weld, and low carbon steels which are not hardenable, but easy to
weld. Mild steel has pretty low carbon, but if it is made from scrap it may
contain traces of all sorts of alloying elements.