This photo illustrates something well. The banners at the top of the photo contain the coats-of-arms of the individuals who bear them. In the middle part of the photo there are those sort of dorky looking statues standing on top of the helmets. THOSE are crests. (They are placed at the crest of the helmet…get it?) The two terms are NOT synonymous. Many people use the word crest to mean a coat-of-arms. I know, those extra two syllables are a killer to have to say! A crest is a part of the full achievement of arms but it may be depicted alone. However a coat-of-arms and a crest are different things.
How correctly put. I am sick of tired of correcting people and then they still go get it wrong. Sometimes it is easier to explain that I am Marilyn Monroe!!!!!