They are related, but even being smart and having smart, dedicated parents isn't enough. You also need to be motivated and have staying power.
I know so many smart, but unmotivated people who drift through life, rarely achieving anywhere near their potential. The same goes for people, like me, who get bored too quickly, and can't manage to stay dedicated to any one subject for long.
I can theorize one "sign" of innate smartness. When I was pregnant, my hands at one point in the pregnancy came to rest on my belly, and at some point, I happened to tap on my belly, and back came the same number of kicks or punches. I thought this had to have been coincidence, so tried a different number of taps, only to have that number tapped back, and so I tried a third number, which again came mirrored right back to me. It was at this point that I became freaked out and did my best to keep my hands off my belly for the remainder of the pregnancy. I have only heard of one other woman having this experience, and she told me her child is also one with a rather high IQ.
Rolling over soon after birth might be another such indicator. Our son did this as a newborn and I've heard other mothers of high IQ children (not just one other, but several others) say their children did the same. One would think such a move would have more to do with muscle strength (and our son was born a typical 7 pounds and 6 ounces, so no football player baby) but perhaps it's more how quickly the mind can figure out how to pull off the turn, I don't know.