A distinction may be considered unnecessarily fastidious. Nevertheless, an emblem is a pattern that is used to represent an idea. More specifically, an emblem is a pictorial image, abstract or representational, that epitomizes a moral truth or allegory. An emblem crystallizes in concrete, visual terms some abstraction: a deity, a tribe or nation, a virtue or a vice. An emblem is an object or a representation of a object. An emblem may be worn or otherwise used as identifying badge. A metal emblem of a cockle shell sewn onto the hat identied a medieval pilgrim to the shrine of Sant'Iago de Compostella. In current American usage, a police officer's badge refers specifically to his/her personal metal emblem sometimes with a uniquely identifying number or name on it, while the woven emblems sewn on his/her uniform identify all the members of that particular unit.
A symbol substitutes one thing for another, in a less concrete fashion: the Christian cross is a symbol of sacrifice; it is an emblem of the Crucifixion. A red cross on a white flag is the emblem of the Red Cross. The Red Cross is a symbol of the humanitarian spirit.
The Crescent shape is a symbol of the moon; it is an emblem of Islam.