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As coincidence would have it, I just happened to be reading The Jeffersonian Gunboat Navy by Spencer Tucker. During the ARW there were two terms used for these ships. One was ""gondola"" (apparently not to be confused with the gondolas of Venice) and the other ""galley"" but he makes no mention of ""row galley."" Tucker is basically comparing ""gondola"" and ""galley"" as ancestors of ""gunboats"" that appeared during Jefferson's time as president. 
However, I too have seen the US Navy using all three names: ""gondola"", ""galley"", and ""row galley."" at random. Most of these terms are found in the various articles contained within DANFS. 
What needs to be said though is that I've found Tucker's works to be a bit sloppy and often lacking in full explanations. He tends to gloss over descriptions that really should be explained completely for clarity.   "