Why is stainless steel "stainless"?

Inox steel is stainless because it does not stain, but is stain the same thing as rust? I just want to understand since stain reminds me of clothing stains, for instance, and I am rather curious as to why one would call inox steel stainless steel. Where does the term come from?

I've just found http://www.stainless-online.com/why-stainless-steel-stainless.htm
(Nov 10 2014, Edit: The link is now obsolete)

It doesn't explain what I want to know. Is stainless steel an American word? Would a Briton call inox steel, ‘stainless steel’?

Wikipedia says of stainless steel that stainless steel is "also known as inox steel or inox from French inoxydable".

As is well known, and mentioned in Wikipedia, stainless steel stains less easily and rusts or corrodes less easily, than ordinary steel, but it is not stain-proof and in some conditions can rust or corrode or give such appearance. For example, after a stainless steel surface is cleaned with steel wool rather than brass wool, it may develop rust stains.

Etymonline gives a 1917 date of origin of the term and says stainless steel is "so called because it is highly resistant to rust or tarnish." Edit: memidex.com tabulates definitions of stainless steel from a dozen sources, two etymology references, and several audio links. Wikipedia includes part of a 1915 New York Times article that refers to "a stainless steel" that is "claimed to be non-rusting, unstainable, and untarishable" [sic] which at least partly confutes the "stains less" etymology of stainless steel, which is suggested in the stainless-online.com link in the question.

With respect to American vs. British usage of stainless steel and inox steel, ngrams shows little difference between the corpuses, and in both cases inox has nearly no usage compared with stainless steel:

A

B

Generally it's known as stainless steel, sometimes in engineering it's called corrosion resistant steel but if you are being that specific you would just use the alloy number anyway eg. 316-Steel.

I suspect stainless rather than rust-free because it was originally expensive and mostly used for cutlery or jewelry rather than engineering applications.
"Stainless steel" presumably appealed to housewives familiar with stains rather than engineering corrosion and stainless-steel has a nice ring to it. The first stainless for household use was marketed by its English inventor as Staybrite.

Don't know who first used the word stainless - there are 3 main types of stainless steel and each form was invented almost simultaneously in Germany, England and America.

Stainless steel is in use in both varieties. Etymonline gives its origin as

1917, a chromium-steel alloy (usually 14% chromium) used for cutlery, etc., so called because it is highly resistant to rust or tarnish.

I think of stain as a more general term, which can refer to any sort of blemish or discoloration. It tends to connote that the discoloration is permanent or at least difficult to remove. A clothing stain is one example. Rust or corrosion on a piece of metal is another. It doesn't necessarily have to refer to undesirable discoloration: stain also refers to the process of staining wood, for example to make a cheap light wood look like an expensive dark wood.

However, in the case of metal, most people would probably prefer to use rust. Stainless steel, as others have suggested, was probably chosen as a marketing name because it sounds better.

In the U.S., "stainless steel" is the standard term for this material. I had never heard the term "inox" until your post.