So if I'm allowed to rephrase what you're saying:

Smart = Brain capabilities. Basic (effortless) use of storage (memory)

Intelligent = Independent/creative use of brain, regardless of capabilities.

I'd say the former is innate, while the latter depends a lot on surroundings and circumstances. Part of forming your personality.

"Come out and take it, you dirty, yellow-bellied rat, or I'll give it to you through the door!"

- James Cagney in "Taxi!" (1932)