I suspect that smart versus stupid is actually about mental stamina. Thinking requires less effort for some people and more effort for others. If you can't withstand much thinking at all, you tend to come up a bit short, and your thoughts and actions will be poorly deliberated. Isn't that basically the definition of stupidity, at least if you exclude otherwise smart people with an impulsivity problem?
@Stoori For me, the solution isn't always instant, but there are light bulbs, mental events that cause you to rearrange the problem, making the solution instantly obvious. After a while, you gain experience and learn to deliberately rearrange the problem. I'm not smart enough for Mensa, but people often call me a genius. I know I'm not stupid, but there are thousands of people with PhD's out there who are much smarter than me.