Yup, Stainless steel simply has Chromium added to the steel for corrosion resistance. Tool steel is also higher in chromium but not high enough to make it stainless. Now also keep in mind the name, it is Stain Less steel, not no stain or no corrosion. Under the right conditions will stain/corrode. Most stainless is softer on the Rockwell hardness scale than carbon steel and it tends to take a less keen edge. The key is how it is tempered. The good stuff is ice or cryogenic hardened. Most of my stainless knifes are cryo hardened and have a 58-62 hardness.

I have both, and as long as it is a properly treated stainless it will give you a good shave. As others have noted they can tend to take a few more passes on the hone but tend to hold their edge better. Now is that the hardness of the blade or simply because the steel does not oxidize like carbon steel so the edge stays fresher longer, I dont know. You will get a good shave from either and if you live in a high humidity location or do something silly like keep your blades in the bathroom where they get steamy and stay damp then stainless would be a very good option.