If you look up the definition of steel you will find something along the lines of "an iron alloy containing more than 0.1% carbon". If you look up the composition of most Stainless Steel you will find that the carbon content is limited to less than 0.1%. Therefore, Stainless Steel is technically not steel. Why is the carbon content of Stainless Steel limited? Well, if you mess up the heat treatment the carbon likes to combine with the Cr to form chromium carbide which has the formula Cr23C6. This compound forms along the grain boundaries (not defined here) and robs the regions along the grain boundaries of Cr. However, Cr was added to the material to make it corrosion resistant so if you remove it the Stainless Steel is no longer stainless. That is why the carbon concentration of Stainless Steel is limited. So Stainless Steel does not contain much carbon to make sure that it remains stainless. What is the result? Carbon is responsible for making steels hard so they hold a really nice cutting edge.
Therefore, Stainless Steel is not very hard and makes lousy cutting tools. Well not really. Metallurgists figured that a metal that was both stainless and held a decent cutting edge would be great so they developed some Stainless Steel that held a fairly good cutting edge. In the US, these are the 400 series Stainless Steel. The key is that, through careful control of the composition and heat treatment, you can create a metal that is a good compromise between corrosion resistance and hardness. However, it you make a mistake in either one you end up with a material that is too hard (brittle) or too soft (won't hold and edge). Generally, cheap Stainless Steel tools such as knives err on the side of too soft while high quality tools generally are right on or err on the side of too hard.