Typically “mixed reality” is used to mean mixing your vision with virtual content. Whereas, “augmented reality” has typically meant displaying a live video feed on a single screen.
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.
"Mixed" versus "augmented" reality have no real meaning, which is why there is confusion about which of the two modalities you're referring to.
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.
The term "augmented reality" was coined to refer to see-through heads-up displays. Pilot synthetic vision system HUDs have been referred to as augmented reality for decades.
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.
I haven’t yet seen a phone Augmented Reality app described as Mixed Reality. I have seen HoloLens, Meta Quest 3 and Apple Vision Pro described as Mixed Reality and Augmented Reality.
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.