Ah, this is the first time you've included "intended context" that I can recall. That actually clarifies a lot. I can see your point, but don't agree that intended context is necessary for application. If the skill being developed is fighting skill, it can be applied in many contexts, and all of those are application. The purest application would be whatever context the individual has in mind, but the broad skill can be applied elsewhere, which is beneficial to development.
I'm not arguing semantics, actually. We literally mean different things when we say "application". You keep bringing that word up. I specifcally try to avoid it because I know we don't agree on the definition, and stick to words we should be able to generally agree on.
Is "sparring" vague? Yes. So is "competition". Can either be beneficial to development? Yes, and sometimes in similar ways. Because they can be using identical rules and have much of the same context, depending how they are approached. I see competition as (potentially) the apex of sparring, rather than something different from it.
I'll go back and look for the post with the groups and see what I think of it.