I think "mixed reality" is the marketing term for augmented reality. Easier to understand for some people.
They are two quite different experiences and use cases. Once both are common it would make sense to call both augmented reality but I haven’t heard any better terms for describing the difference to people yet.
My question is why avoid the terms overlay, superposition, display and even vision? Why instead purport to have altered reality?
Traditionally in aviation and the military they said "heads up display", because they can't afford to be obtuse. The display allows the pilot literally to keep their head up, instead of pointed down at their instruments. And I'm sure there was no truck for anyone who would have called it mixed or augmented reality.
x = real world y = virtual world
Best I can tell, mixed reality is augmented reality, but with mixed interaction. You hit the fake ball with a real bat in mixed reality and it bounces off the real wall. Maybe you even feel it hit.