They both have similar meanings and can have the same meaning in some sentences. However some sentences that use "smart" imply expert knowledge. While "clever" does not necessarily mean expert knowledge, but can imply that a person is cunning, or thinks in a different, better way. So a smart person can be someone who gives a textbook answer to a question, while a clever person might come up with a different answer that is unconventional, but will logically make sense and work.
all smart people are not clever. all clever people may not be considered book smart, but they will be considered some kind of smart depending on in what area they are clever.