Jim,
I am by no means an expert. In my research for my Fulton project the Roosevelt Steamboat was always referred to as the "New Orleans". I suspect that it could have been contracted to "Orleans" much in the same way that we refer to the North River of Clermont as the "Clermont". Here's a link that I filed:
Nicholas Roosevelt's 1811 Steamboat, Dahlinger's account It gives references etc.
Sternwheel/Sidewheeler??? I also attached 3 PDF files. From what I have found it appears that the New Orleans was a sidewheeler which would have been in line with Robert Fulton as her designer. Except for Gary Lacy most rederings including the replica show her as a barge type river boat. For some reason Gary Lacy chose to depict her as a twin to the North River. I have written to Mr. Lacy to ask where he got his information. He has yet to respond.
I haven't found many definitive answers for the description of the North River or the New Orleans. Back then they most likely used conceptual sketches as a start and then designed on the fly without recording the details. This all adds to the confusion for anyone trying to build a model or paint a painting of these boats.