A theory is an established and respected explanation of a natural phenomenon, acquired through confirmation of its principles through the scientific method - testing, confirmation, and observation and experimentation. Evolution is a widely accepted and demonstrated theory, validated across many disciplines.
A proof in science a successful demonstration of a hypothesis under study using evidence and analysis. It is a misconception in many ways, since science actually can prove nothing. In this sense, "proof" is a simplified way of saying "greatly enhanced confidence".
Quoted from Rick Thorne on Quora - link.