Intelligence and Smart are almost the same thing because when you're intelligent you're smart.
But intelligence is actually something you're born with and also a measure of your IQ and being intelligent means that you can learn new things rapidly unlike when someone is just smart.
When you're intelligent you have a more powerful brain than a normal smart person since intelligent people grasp new things much easier than some other people.
If you can code a website and database or program a computer then I would say you're both smart and intelligent because even though I'm smart I could never grasp programming a website or writing a mysql database or even programming a computer.