Academically speaking, if a student has achieved a lot and has been performing well in a lot or maybe all subjects, then it's safe to say that he is smart. Some people learn faster than others. Some are really critical thinker and some can solve mathematical problems with so much ease. Others are very articulate and can speak different languages in front of a crowd. Obviously, these types of performances would automatically reflect on their grades. They often graduate with honors and would receive a LOT of medals to recognize their intelligence and diligence.
Another example is being "street smart". These people knows a lot in this world because of the environment they grew up with and their previous experiences. You can't fool these people because they're definitely wiser than you. You might think that you're smarter than them, but think twice. They know more things in this world compared to you. They're strong individuals who can always find solution on real-life problems. Whatever challenges they may face, they remain to have a positive outlook and would remain calm as they solve their problems. They know how to deal with hardships and they have tons of strategies and techniques to back them up.
Always remember that we are all smart. Being less successful than others doesn't mean you're less intellectual. Remember all those times you've surpassed the hardships in your life. Remember all the problems you've solved. You just have to develop the intelligence that you have because that would also help you grow in life. It's going to be one of your strongest armour in life. Never think that you're not as smart as others. You are smart enough to survive this world. You are smart enough to overcome every problem that comes your way.