High carbon steel is the original blade steel. In its most basic form, steel is a properly balanced alloy of iron and carbon. Other elements are often also present and may have a significant impact on the performance characteristics of the alloy, but the carbon is what enables the steel to harden, and that hardenability is what makes steel so ideally suited for cutting implements. The higher the carbon content, the more hardenable the steel (up to a point). Thus “high carbon” steel.
Stainless steel alloys also contain carbon, but there are relatively high concentrations of other alloying elements that make it stainless. Chromium is the most common one. While modern technology is developing better and better stainless alloys, the general rule of thumb is that high carbon steel makes a superior blade.