[brendev]

I think your question is getting into the field of martial arts lineage. People might have their own narratives/ mythologies around this, but here's the most neutral way I can explain it: As techniques and styles evolve over the years, people come up with new names to describe those styles. Name similarities will often imply closer ties in lineage.

As a Brazilian Jiu Jitsu practitioner, I cringe when I see it spelled any other way, but also I have to recognize that I only feel that way because I have more exposure to that specific martial art/spelling.

[toastal]

The spelling ‘mistake’ makes it easier to web search.