Here I was thinking all this time there was only one "Round-Nacelle" we were dealing with, and then I check Bernd's Wolf 359 ships write-ups to learn there are two. Stupid Wolf 359. Write-up by Bernd. No diagrams.
Round-nacelled ship I The Art of Star Trek shows photos of the two wedge-shaped prototypes originally built by Ralph McQuarrie for Star Trek Phase II back in 1977, until it was decided to further develop Matt Jefferies's original design of the Enterprise. The book states that these two models were among the ship wrecks at Wolf 359. The more compact of them can be seen at the Qualor II surplus depot in TNG: "Unification, part II". This is remarkable in that the scene as a whole is indeed a re-use from the Wolf 359 graveyard TNG: "Best of Both Worlds, part II", but the round-nacelled ship was not in the corresponding scene at Wolf 359. Considering the statement in the book and assuming that there is probably unused stock-footage from BoBW, we believe that the take of the round-nacelled ship was originally made for BoBW and then inserted into the foreground for "Unification".
Known round-nacelled-I ships: No name or registry known
Occurences: TNG: "Best of Both Worlds, part II" (not visually confirmed) TNG: "Unification, part II"
Note: As for the ship's name and registry, we can't tell anything. The Art of Star Trek shows an unlabeled model, and if it was ever labeled, it would have been "U.S.S. Enterprise NCC-1701", so we don't really want to know.
Round-nacelled ship II The Art of Star Trek shows photos of the two wedge-shaped prototypes originally built by Ralph McQuarrie for Star Trek Phase II back in 1977, until it was decided to further develop Matt Jefferies's original design of the Enterprise. The book states that these two models were among the ship wrecks at Wolf 359. The more streched of the two ships has not been visually identified anywhere, so canonically it doesn't really exist so far.
Known round-nacelled-II ships: No name or registry known
Occurences: TNG: "Best of Both Worlds, part II" (not visually confirmed)
Note: As for the ship's name and registry, we can't tell anything. The Art of Star Trek shows an unlabeled model, and if it was ever labeled, it would have been "U.S.S. Enterprise NCC-1701", so we don't really want to know.