Proof is used when you are demonstrating that a certain statement is true, for instance you could offer a demonstration (proof) that a mathematical assertion holds; in this case you will never use the term "evidence". Other sciences do not need full and complete proofs, but get along with a theory until evidence is found suggeting the theory is false in its prediction; evidence is the collection of facts and logic concatenations (syllogisms) that suggests that some theory, hypothesis, statement to hold true; evidence is important in all sciences, as it clearly points the direction of further studies, therefore, in the "lucky cases" leading to further evidence or more articulated hypothesis.

Evidence shows that something might be true. Proof shows that something definitely is true.

I don't think there is one. Proof means "evidence sufficient to establish a thing as true, or to produce belief in its truth." Whereas evidence is the thing itself you're trying to prove. Evidence "that which tends to prove or disprove something, ground for belief, proof." If you go to court and claim someone backed into your car, but you have no evidence, you won't have a fun time. If you claim to have discovered a new type of dinosaur, people will want proof.

Thanks. It's because some dictionaries tell almost the same meaning of two words and this confuse me....

My advice buy an oxford dictionary