I wouldn't say there's any fixed standard to measure intelligence by, but rather grasping your own limitations and critically understanding your potential is how we should look at it. It's a bit antiquated now to refer to the left/right dichotomy of the brain but I can say, for certain, that I'm just not wired for ratiocinative reasoning, I'm pretty sure I've got dyscalculia because numbers just trip me up at the best of times and I'm really disordered. However, that also means I'm really good at associative thinking and intuitively understanding concepts and recognizing symbolism, etc. There's also emotional intelligence. Being empathic and compassionate is definitely a learned skill and not innate in all of us. That's more of a philosophical question for another day.

Genius comes with passion, for the most part, or having an ego defying experience or series of experiences to recalibrate your self because once you realize that there is no tangible self and that you're just an amalgamation of your own memories and influences then you can explore your own talents to the fullest extent. Also on your mulling whether there's a fine line between genius and stupid I immediately thought of Karl Pilkington. I remember somebody saying he's like an RPG character that's had all their points pooled into wisdom and none in intellect. So there's plenty of informally educated people that have reached the same conclusion as academics on many concepts but they just don't have the mental lexicon of tying it all together.