They are not one and the same - there is still the _presumption_ of innocence when being found not guilty. Not guilty means that you were not _proven_ to be guilty, not that you have been proven to be innocent. You are equally not guilty even if it's pretty clear you did it but there is not quite enough prove, or if proven you didn't do it. You are free from liability under the law, but you are not necessarily factually innocent.

Incidentally, this is largely why Scots law verdicts of acquittal -- "not guilty" and "not proven" -- reflecting the two standards of not guilty. "Not proven" carries the implication that the jury is not convinced of the defendant's innocent, but there is not enough evidence for conviction.