IANAL, but
is the correct definition of what a jury finds. A jury decides if the prosecution/plaintiff has met their burden of proof.
Whether society should or shouldn’t hold someone who was acquitted as innocent depends on the facts, and as you note, people are entitled to their own opinion in the matter.
In some cases, people who are acquitted didn’t do it.
In other cases, people who were acquitted did do it, but the prosecution couldn’t prove it in a court of law.
I’m a little confused about your confusion. This statement:
is just what you say if you believe that the person who was acquitted did do what he was charged with. It’s a subset of the possible reasons someone could be acquitted-and is meaningless statement unless an acquittal doesn’t require a factual finding that the defendant didn’t do what he was accused of doing. If acquittal requires a factual finding of innocence, there aren’t any people who were acquitted but still did it (if juries get it right)
On a related note, there is (AFAIK), only one court system where the distinction is made. Scots law has three verdicts a jury can give: “Guilty”, “not guilty”, and “not proven”. The first is a finding of guilt, the second is an acquittal and a finding of innocence, and the third is a simple acquittal.
This is only true when you’re talking about the presumption in a court of law/in the eyes of the law. O.J. is presumed to be innocent of the murders after his acquittal so far as the criminal justice system is concerned. Private citizens can hold any opinion they care to in the matter.