TBH using the same word to describe both doesn't do justice to the difference between what VR does and what 1st person view on a monitor does. It's not different magnitudes of the same thing. It's just a different thing entirely. I like the word "immersive" and I think in a literal sense it's very descriptive of what VR does, but decades of use and marketing speech for products that are anything but have inflated the word to a point where it hardly means anything.
"Presence" is another word that has gotten hold in recent years when describing the literalistic, encapsulating sense of "being there" that VR gives you, perhaps we should use that instead, as "immersion" kind of gives people the wrong idea.
