Vanity and pride are different things, though the words are often used synonymously. A person may be proud without being vain. Pride relates more to our opinion of ourselves, vanity to what we would have others think of us.
JANE AUSTEN, Pride and Prejudice
To say that a man is vain means merely that he is pleased with the effect he produces on other people. A conceited man is satisfied with the effect he produces on himself.