As per wikipedia:

> The term carbon steel may also be used in reference to steel which is not stainless steel;

And if you want to talk about carbon content, standard separates it further:

>Carbon steel is broken down into four classes based on carbon content:

>low-carbon steel

> medium-carbon steel

> high-carbon steel

> ultra-high-carbon steel

So while you might mean steels other than low carbon steel when you say it and it's how you understand it, that is too broad of a name to define specific steel in the American standards for steel (SAE, AISI). Carbon steel is any steel with between 0.05% of carbon up to 2.1% of carbon content, so that name includes everything from low carbon steel to ultra high carbon steel..

Edit: and some stainless steel types can be right on that 0.05% limit, but most commonly they're under it. That is why carbon steel is used to differentiate steel which rusts from stainless steel.

I see lots of people downvoted my previous comment, so clearly there's a lot of confusion regarding this and people throw the name carbon steel on whatever suits them in their context.