To be totally honest, I am not sure what exactly draws the line between banjo, and ukulele. I'm not so sure it is the scale length, because how would you explain a baritone uke? I think it has more to do with the way it is tuned. Banjo strings are a completely different tuning than a Uke. I am SO far from being a pro. I don't even know, or even understand music theory. I am simply a musician/music enthusiast. I gone down the musician path of most resistance. We have had this conversation before about "therory/no therory" is it needed or not? I believe not, even though, with it, my journey would have been much easier. My abilities are raw natural abilities, and being able to pick up melodies from the sense of hearing. I can hear something and just tell if it is sharp, flat, or the wrong note, or key, even if I don't know what that note, or key is. Not so fantastic though, many can do that. It's just a tuned ear I guess. As far as restoring vintage banjos, I just love to do it. I am no Luthier, but I love to restore banjos because they, unlike any other string instrument are pretty modular. I think they are the only one you can just take completley apart, repair/replace/clean individual parts, and put them back together and play them. I have restored several over the past few years, and love it.
But at any rate. Again, I am not sure what makes a banjo Uke a banjo uke and not just a banjo. My Banjo uke is small like you would expect (about 22" long), and it is tuned just like a Ukulele but has that fun tinny, banjo sound. So, I would think that being strung like a Ukulele, and ukulele strings, and tuning, is what makes it a banjo uke.