as most ppl have said here there are a lot of different aspects to intelligence. there is a memorization aspect, a way to apply said knowledge, a way to adapt the knowledge (this is something most ppl lack), a creative aspect, a spacial aspect (another thing ppl lack) and also the ability to learn (different from memorization)
a nice question i always ask when someone says "oh i have a high iq and i'm smarter than you" is i simply ask them to describe a cup sitting on a table to me or navigate themselves around a city when they've messed up the directions and need to get back on course but can't turn around. most ppl can answer a logic problem however those last two problems have them stumped and they will even go as far to say "no that's not intelligence" but really it is, it's just not as simple as a math problem
a nice question i always ask when someone says "oh i have a high iq and i'm smarter than you" is i simply ask them to describe a cup sitting on a table to me or navigate themselves around a city when they've messed up the directions and need to get back on course but can't turn around. most ppl can answer a logic problem however those last two problems have them stumped and they will even go as far to say "no that's not intelligence" but really it is, it's just not as simple as a math problem