Stupid is consistently making poor choices and not listening to advice from others when those poor choices run amok.
Not smart is not intuitively knowing what to do in a given situation - this can be learned away - it won't give you the intuitive answer, but at least you'll know not to do something in a given circumstance.
I have this tab open from a procrastination session some days ago:
http://harmful.cat-v.org/people/basic-laws-of-human-stupidit...
I like the definition of stupid vs. intelligent from there - intelligent person consistently makes win-win decisions. Stupid person consistently makes lose-lose decisions, inflicting loss on other people for no gain for themselves.
I've always thought of "stupid" as different from "not smart". I can't fault people for not having the experience or knowledge that I or others have. I tend to think more of an "active stupid" as a lack of common sense, and making actually poor choices as opposed not making good ones.
To me, it's more the difference of "My laptop is overheating and I can't figure out why" versus "My laptop is overheating so I poured water on it to cool it off."