Smart and intelligent are completely different.
If you're intelligent in some field, it means that you can use your brain in that field and do something new and innovative. (Solving sums, however tough, doesn't always measure intelligence; similarly, IQ tests cannot measure intelligence.) For example, both Einstein and Beethoven were intelligent in their respective fields. When a person is called "intelligent" in general, it indicates intelligence in his/her field of excellence.
Smartness is an adjective for a person as a whole. Your dress, your behaviour and your character together determine whether you're smart. It is independent of intelligence. There are many people who are smart, but do not have any intelligence in any field (or in another way, have not been able to find the field in which they're intelligent). People who are not so smart, may be very intelligent.
Nowadays, teachers advise to study "smarter" and not "harder". For example, a student who memorises sums from the textbook will get more priority than a student inventing something in that field. This happens at least in school, where intelligence is defined by marks. The first student is smart, the second is intelligent.