In some cases it may be semantics, but that could be the many ways we've decided to use it. Part of my exposure to it came when people were talking about laws. Tell the truth is about perception, what you know, and a lot of other things.

"The whole truth, nothing but the truth"

Facts are specific details that do not change depending upon who observes them.

So as in my image.

"Truth is truth even if no one believes it"

This is inaccurate. Your truth and my truth may both be true as far as we are concerned, but not the same truth.

"Facts are facts even if no one believes them."

Is an accurate statement and I believe is the intent of the original statement.

With the word truth you do not know which aspect they are using. Some people use it interchangeable with the word Truth. Yet, then other times "truth" means something else. It is very different from Fact.

If a person must use Truth then it would be more like a super set at this point. It could contain facts. Yet it could also contain things that have absolutely nothing to do with facts.

Truth turns out is subjective.
Facts are perhaps more objective.

The key thing in truth tends to be that the person "believes it".

That doesn't make it a fact.

The facts may show that this man was in the visinity, fits the description of the culprit, fled from police when confronted, etc. All these facts lead to a false conclusion.

Yes, but that was not due to the facts. That was the "truth"/conclusion that the police chose to draw from those facts. That truth is based upon more than just conclusions. It will also be based upon biases, and assumptions.