Intelligent and Smart

Intelligent

Someone described as intelligent has good understanding or a high mental ability. It can also describe an action taken with a good understanding of the results. Intelligence is the noun form and is high mental ability or specialized information.
Ex: Fran discovered that being intelligent and having high exam marks was not enough to be accepted to study at Oxford University. She was rejected because she didn't participate in any school activities.
Ex: Military intelligence is information or knowledge about the people and activities of enemy forces, and it is used to determine if or when they might attack.
Intelligence Quotient or IQ is a measurement of intellectual ability determined by the results of a test whose median score is 100. Artificial intelligence, or AI, is intelligence exhibited by machines, especially computers.
Ex: An IQ score is a sometimes disputed measurement of a person's intellectual ability. Some claim the test is biased and does not predict how well an individual might perform in academic subjects.
Ex: Ken Jennings and Brad Rutter, men who have won the most games on the TV show Jeopardy!, played against and lost to Watson, an IBM computer with artificial intelligence.

Smart

A smart person has or shows quick intelligence. Smart can also mean fashionable.
Ex: Colin is a smart football player. He is able to see every other player's position on the pitch in a fraction of a second, so he can safely pass or shoot the ball before the other team knows what he's doing.
Ex: Edith Head was an Academy Award-winning costume designer who created smart outfits for some of the most famous film stars, including Elizabeth Taylor and Sophia Loren.
Smart as a whip means very intelligent or quick-witted, and the expression probably comes from the sharp crack that a whip makes. Even though it is mainly a North American term, its meaning would be understood by British people. And a smart aleck is a wise guy or an irritating person.
Ex: My new kitten is as smart as a whip. She's already litter trained, and she fetches the catnip mouse when I throw it.
Ex: Tommy is not only a bully on the playground, he's a smart aleck in the classroom, always talking back to the teacher. As a result, he spends a lot of time in the principal's office.