What is the difference between a formal and an informal proof?

 informal proofs are usually in paragraph form, while formal proofs are numbered, like this: 
Given: a=b, b=c 
Prove: a=c 
1. a=b, b=c 1. Given 
2. a=c 2. transitive property 
the first line is usually the given, the middle lines are statements which help you get to your proof, and the last line is your proven statement. next to your statements, you have to give reasons why the statement is true, like a=c is proven because of the transitive property