I thought high carbon steel simply means a steel with enough carbon to harden to 60 HRC (as opposed to mild steel). Which would include 5160, 440A, AUS6; and exclude 420J and other steels with less than 0.6% carbon.
There are several ways to classify steel, I think of them as basically two types: simple carbon steel, and alloy steel (greater than 5% alloying elements other than the usual carbon and iron). The simple carbon steel include the 10xx series, the S series, 5160, L-6, 52100 etc.
Alloy steel would include the CPM alloys, M-2, A-2, D-2, 440 series, ATS-34 and the like. Steels are alloyed for different reasons; M-2 is designed to stay hard when red-hot, CPM steels are made for extreme edgeholding, A-2 is made for easy industrial air hardening. All of them are more stain-resistant than the simple carbon steels. But there is a whole family of steels alloyed to minimize oxidation ----- the so called stainless steels.
Basically simple carbon steels are known for their strength and toughness, (which is why they're used for car springs and construction) as well as easy sharpening. The alloyed steels are known for their performance according to their designed use.