What is the difference between a crest and a logo?

Answer 1

A crest is a historic term meaning the figure, animal or other item worn on top of a knight's helmet during the late medieval period. This also served as a kind of badge which would appear on his standard (if he were of sufficiently high rank), or on the tunics of his servants and men-at-arms. The crest might also be shown on his seal. It was considered to be a part of the coat-of arms, even though it did not appear on the shield, and was part of the grant of arms awarded to the knight by the college of arms.

A logo is an extremely modern badge, shape, sign, word or combination of these used to identify a particular marketing brand. It has very little history and has nothing at all to do with the medieval period; it is entirely related to the retail or marketing industry.