Thanks to the podcast of Morgan Housel. He made my thoughts clear. Now, I put my own thoughts herewith.
Intelligence is about learning a new subject quickly. Understanding complex Physics. Solving Math problems at a great speed. Intelligent people have logical approach to everything and are good at reasoning. But they struggle with communicating it to the ordinary people. They easily get bored and stay away from it.
Being smart is about showing emotional maturity. Reading people accurately. Understanding the situation and handling it smoothly. Showing tolerance even when disagreeing with people. They can handle illogical & irrational people and situations without getting stressed. It is difficult for them to gain mastery over a single subject. Rather they would like to manage the experts.
You can find people with high intelligence working in the laboratories, or being astronauts in the spaceships. You can find Smarts becoming managers of big corporate firms and leaders of the social movements.
Intelligent people have a higher risk of becoming lazy and good for nothing. You don't find all of them working hard. Smart people, when they lose integrity, can easily become manipulating politicians and make the society work for their selfish motives.
Thus, being intelligent or smart comes with their own benefits and risks. You can't find people who are both intelligent and smart. They are rare. Usually one character becomes dominant. Most Nobel Prize awardees do not have a long list of friends. And those who have a wider social circle, can't digest a scientific article. So, it is either this or that and can't be both.
If you can do an honest review of yourself, you can find the dominant trade within you. You can also observe what comes naturally to your kids. You can groom them to relevant professions and also keep an eye on what would bother them.
If you like solving wizards and are blamed for not having friends, it should be fine. Remember, those who blame you would need calculators even for simple calculations. And those who can gel with all kinds of people, can't be blamed for having poor grades at school or lacking taste for any fine art. That is not their domain.
Finally, if you don't care whether you are intelligent or smart and you are happy both ways, you are a third category - a Buddha.