“Say one comes across a fruit tree in the woods or finds a valuable object in a public place. In both instances, one is taking, if he does, that which is not given.”
We can clarify these by looking at the “intention” (whether there is greed involved), and also “whether anyone will be harmed by a given action”. That is the bottom line.
In the case of the fruit tree in a forest, it does no harm to anyone to eat a fruit from it. So, that is not theft.
But in the latter, there is someone who lost that item. So, if there a “lost and found” office at the public place, one should return it there.
But if one finds a valuable thing lying on the road, say, then it is fine to take it, unless there is a way to find the owner. If it is really valuable one could give it to charity on behalf of the (unknown) owner.
So, depending on the situation, we can figure out what to do.