Manners is all about showing respect to others. We say please and thank you because it is polite and it shows that we consider other peoples feelings and care about others. Manners are about those small niceties where we put others first.
Etiquette can get much more detailed. During the reign of Louis the XVI of France he tried something a bit knew. In France at this time the monarchy was in the process of increasing their power. They were God's chosen to lead after all. He was afraid that some of the gentry and nobility would forget their place. So he established elaborate rules of etiquette. He would throw balls and parties where you had to where elaborete clothing and behave in certain ways. Soon each house tried hard to make sure they were the best in line with these knew rules. Soon the families feuded among themselves and no one could get along well enough to conspire against the thrown. Etiquette became about making sure that you are in the proper rung in society. It just became a presuit of self and not thinking of others.
We need to be civil ourselves and have proper manners and we need to teach these manners to our children. So that we can keep our society together and unite. But if we care to much about the societal rules it can serve to tear us apart and not pull us together.