As part of my backlog of words, evince roused the lawyer in me today.
Evince comes from the Latin "e" meaning "out of, from, or thoroughly" and "vincere" meaning "to conquer". And somehow "to conquer thoroughly" now means "to show clearly". More trial by combat. Compare evidence which comes from the Latin "e" and "videre" meaning "to see". So in this instance, "to see thoroughly" means "to show clearly". This is just the blind leading the blind. Amazing how two completely different etymologicial roots can come to the same alleged usage. Well, almost. Say it with me: there are no true synonyms.
Ok, so what is the difference. Since evince comes from to conquer, it is a personal activity, therefore, the things shown are personal traits or qualities, not impersonal facts. And while it expresses the traits and qualities of humans, it may expand to animals or inanimate objects as these may exemplify human traits or qualities. The miscreant youths evince their low aspirations by loitering in the mall. I evince sympathy with my eyes alone. I evince cold. No. I evince that I am cold. Yes. As a result of his last favorable jury verdict, Plaintiff's counsel evinces haughtiness. My cat evinces her distaste for her food by ignoring it. Yes, because she has such personality. Lions evinces their superiority in the jungle with a loud roar. Yes, because we ascribe human qualities to "the king of the jungle". My stereo evinces life-like sound. Probably as it mirrors human sound, but the better word would probably be evoke. Meanwhile, evidence demonstrates a fact, but is employed solely from the non-human perspective. My cat evidences that she is hungry by sitting at her bowl and yowling. Yes. He evidences that he is annoyed by scowling. No. The bills in the box evidences that the mailman delivered the mail today. Yes, although as an issue of circumstantial evidence, the better word is indicates. Plaintiff's counsel's haughtiness evidences his last favorable jury verdict. Yes, but it it's not likely that he won against me.
The trouble with this pair is that evince has been roughly subsumed by other words that don't sound like evidence, and evidence is rarely used as a verb, since when evidence is used, even as a noun, is suggests a legal meaning. Therefore, evidence supplants evince, perhaps as evince may be a malapropism for evidence, and everyone just uses it as a noun to make things clear. The evidence will show that my cat is hungry, that I was was cold, and that Plaintiff's counsel is haughty.