It isn't just physical breath, though, but the life force itself. The concepts arise from within different cultural traditions, but refer to the same energetic aspect of the human being.“Understood differently by their respective traditions” = different concepts.
We aren’t Ancient Rome, there’s no need to tell other people that their thing is actually just a different facet of this other thing from outside their culture.
They’re similar, not the same. And that similarity is most likely largely a result of breath being the starting point of nearly all esoteric traditions that focus on physical movement and forms, because breath is physically central to all exertion of the human body.
So while the concepts might be somewhat different because they arose in different cultures, what they refer to--the actual aspect of the human being called "prana" in yoga and ayurveda and "chi" (or qi) in traditional chinese medicine and martial arts--is the same phenomena.