it is about preference

they both are slangs for clever, people have different preferences in using them.
for example, some people use bright when it is about intelligence, use smart when it is other kind of cleverness (like being manipulative etc). that is why very often times we hear smart politicians or smart bankers, but bright students or bright scientists etc.

when talking about people, if you are not sure which one is appropriate, think about the opposite - smart vs. stupid; bright vs. dim.

here in UK people also use smart for dresses, hairstyle etc. for example, you look smart today; or your new haircut looks really smart etc. etc