Well, for me at least, evidence leads to reasoned and/or probable conclusions whereas proof is undisputable certainty.
In science, it is never possible to have indisputable certainty. One is only ever to provide more and more evidence for an assertion, thus making the conclusion ever more probable.
This is an important distinction because many people have this false idea that they can actually "prove" an assertion in the same way that they can "prove" something in geometry or with logic. This simply isn't the case.
With that being said, what is the evidence that we are not alone in the universe?