What is difference between someone and somebody?

I think someone is used when there is a particular person to whom you are referring whereas somebody is used when you are not referring to a particular person.

Example 1:

Somebody out there loves me.

You don't know who that person is but you know that he/she exists.

Example 2:

Mark: I can do Maths in my sleep

Paul: Well, someone is being cocky.

Paul uses someone as reference to Mark.