honestly, as long as you have fun on the bike, I would not give a damn what to you call it.
I do understand what you try to say, that the style of the bike does not determine the style of the ride, but I think you are too much in the topic, especially in a young sport like street trials, that REALLY started to get a little bit popular around 2008, whereas other sports had decades to do the same.
Wait 10 years, and you will be able to tell the proper street trials from the street. It is too early to argue about the names, especially about a sport that loads of people do