I don't like "Exact Duplicate" in the upper text either.
Instead of
[Possible|Exact] Duplicate:
Was Stack Exchange named after Experts Exchange?
It should read:
Found Duplicate:
Was Stack Exchange named after Experts Exchange?
Rationale
I think the problem here is that "possible" has the association with "likely", "conceivable" and "probable", which seems to contradict with "exact" in the below message.
However, changing the upper message to "Exact Duplicate" does not take into account that the individual close-voters might have chosen different duplicates. And that this actually requires some judgment on their part - individually they are expected (trusted) to pick exact duplicates; but which duplicate they pick is a matter of judgment and the outcome may differ between voters. So, as a whole, not really exact in my opinion.
In that respect, the message "Possible Duplicate" is actually better!
I think we all can agree that "possible vs exact" can be confusing to some. And it can easily be avoided by clearly communicating that the "closers" found the following duplicate(s?).
PS
IIRC, I saw some closed questions with more than one "Found Duplicate" so we might run into a pluralization issue there :).