My uncle in-law, whom I haven't met yet, is guide in the Chicago area (Mike Norris) and I found this in one of his articles (he also does a radio show):

To my surprise the laker took the lure and I was one up on Richard. The next time I caught a fish I turned it loose in shallow water so that I might see if it too would take the lure a second time. I know this is hard to believe but it did and I yelled, "Two up". Richard did not think I should count that fish because I caught it twice. Of course I disagreed and told him, "It takes twice as much skill to catch the same fish twice. http://www.arcticfishing.com/articles/arctic-angling-adventure.php

Does this count as one or two fish?

In a non paper tournament no, even though you can catch fish from your livewell twice, there is only one fish. In a paper tournament, or plain bragging rights it does count in my opinion. But bragging bout it is not suggested.