Or, in other words if you are defining something, you will most likely use "c'est".They are used almost interchangeably in spoken conversation, as far as I understand. The functional difference is related to the notion of topic versus comment. If a person or object has already been mentioned in a conversation, you'll probably use il est/ elle est. (Elle est musicienne) If the person or object is being introduced in the conversation for the first time, you are more likely to use c'est. (Julie, c'est une musicienne)
You can say "he's Matthew", it's probably not as common as "this is Matthew", though.This is pretty much as in English: you would say "Hi, I'm Christina and this is Matthew", not He's Matthew, wouldn't you?