difference between proof and evidence

prove - [transitive] (батлах)
1 to use facts, evidence, etc. to show that something is trueprove something    --- “I know you're lying.” “Prove it!”     2 to show other people how good you are at doing something or that you are capable of doing                something        prove yourself (to someone)            ---- He constantly feels he has to prove himself to others.          proof - (баталгаа, баримт) гол төлөв <information, documents> - гэсэн утгаар     1 [uncountable, countable] information, documents, etc. that show that something is true           ---- Can you provide any proof of identity?     2 [countable] (mathematics) a way of proving that a statement is true or that what you have                     calculated 

evidence - (нотлох барит, нотолгоо, үндэслэл) гол төлөв <the fact, sign, object> - гэсэн утгаар
[uncountable, countable] the facts, signs, or objects that make you believe that something is true
evidence (of something)
     --- There is convincing evidence of a link between exposure to sun and skin cancer.

difference between evidence and proof

• It is not really a difference of abstract versus practical. Evidence is a fact or situation that suggests something might be true. Proof is a fact or situation that removes all doubt. Sometimes more than one evidence can add up to proof.
  
  Fingerprints are proof that a person touched something. If I find your jacket in my car, it is evidence that you were there, but not proof. If the police find lots of money in my house, it might be evidence that I robbed a bank. A videotape showing me at the bank holding the gun would prove that I robbed a bank.

• To have proof you need evidence. If you have enough evidence then you have proof.
  
  For example if the Police were looking for a murderer and they found a man with blood on his hands. That would be one piece of evidence. If they found a knife in his pocket, that would be more evidence.
  
  When they have enough evidence they have proof.

• Evidence is a fact or opinion that might prove some case, it at least supports an opinion. Someone says they saw the killer - that's evidence. The means by which any alleged matter of fact whose truth is investigated at judicial trial is established or disproved. 
  
  Proof - that is when the truth, or as much as we can know of the truth is decided. -- unless you are talking about mathematical proof ... that's different. The act of validating; finding or testing the truth of something