Proof refers to the process of establishing the truth or accuracy of a fact or statement, while evidence refers to any data or facts that can be used to support an argument.

Proof and evidence are related but distinct concepts in the fields of law, science, and mathematics.

Evidence refers to information or data that is presented in support of a claim or argument. Evidence can be circumstantial, testimonial, or physical, and its strength and reliability depend on a variety of factors, including the credibility of the source and the consistency of the information. Evidence is used to build a case or support a hypothesis, but it is not conclusive on its own.

Proof, on the other hand, is a higher standard of evidence that demonstrates the truth or validity of a claim with certainty. Proof can be mathematical, logical, or scientific, and it requires a rigorous process of testing and validation. In a mathematical proof, for example, a set of premises and reasoning are used to deduce a conclusion that is considered to be incontrovertibly true. In a legal context, proof beyond a reasonable doubt is the standard of evidence required to convict someone of a crime.

TL;DR - evidence is information that supports a claim, while proof is the highest standard of evidence that establishes the truth of a claim beyond a reasonable doubt.

One is in the pudding.

The legalities of them I'd assumed

Proof is formal logic, and evidence is akin to bayes’ theorem.

Evidence is like parts of overall proof usually. Like evidence can form a theory or hypothesis but proof gives fact. Proof is also a term for alchemy percentage that goes back quite hundreds of years were to give proof alcohol was strong enough they would test if it was flammable. Now proof is just basically the percentage of alcohol x2.