Are we splitting hairs here?
All steel is an alloy, the phrase Alloy Steel is redundant making stainless steel an alloy of an alloy.
Surprising no one the automotive industry coined the phrase Alloy Wheels, one may produce an aluminum wheel that is not alloyed, it is impossible to produce a steel wheel that is not an alloy.
Are we splitting hairs here? In my book, a steel that is just a carbon steel is not considered an alloy steel; to be considered an alloy steel, usage is that it contains another element, such as tungsten, nickel, chrome, etc. Mere traces of other elements that do not have an effect on strength or durability do not make it an alloy steel.