The practice of law is a lot like doing algebra. The legal rules are the formulae and the facts are the variables and numbers. You plug the facts into the applicable rules and you get a legal result: breach of contract or not, tort or not, guilty or not guilty, etc.
Evidence is the raw material of facts, the things that lawyers present to the court in the hope that they will be granted the coveted status of 'facts'. They are 'fact candidates'. When evidence is filtered through the scrupulous rules of evidence, the survivors are 'facts'.