Don't take this as a definitive answer, but when we did Shuri Ryu, we also did three of those kata, and those that wanted to "go further" and get ranked in kobudo had "other kata" that they did (probably the other three) since they were affiliated with a primarily Shito-Ryu organization at the time. I never heard anyone mention a "style" of kobudo, or "brand", other than "kobudo".
We had a number of people who took rank in kobudo, some specializing in bojutsu and some in "bladed weapons", but all of them only talked about being ranked in kobudo, never mentioning any "style" or brand of it. FWIW
I do remember some of the people who trained with us calling their kobudo "Ryukyu Kobudo"... which would indicate an Okinawan type...
