I am specifically trying to reconcile the wording from the DMG, p.47, with what I know of how planar creatures work.
Traveling through the Astral Plane by means of the astral projection spell involves projecting one's consciousness there, usually in search of a gateway to an Outer Plane to visit. Since the Outer Planes are as much spiritual states of being as they are physical places, this allows a character to manifest in an Outer Plane as if he or she had physically traveled there, but as in a dream. A character's death- either in the Astral Plane or on the destination plane- causes no actual harm... Thus, high-level characters sometimes travel to the Outer Planes by way of astral projection rather than seek out a portal or use a more direct spell.
Which led me in turn to the astral projection spell itself:
If you enter a new plane or return to the plane you were on when casting this spell, your body and possessions are transported along the silver cord, allowing you to re-enter your body as you enter the new plane. Your astral form is a separate incarnation. Any damage or other effects that apply to it have no effect on your physical body, nor do they persist when you return to it.
The wording clashes a little, but the intent seems clear - if you use astral projection to travel to a non-Material Plane, you work the same way a summoned fiend, fey, or celestial works on the Material Plane. You aren't permanently killed so long as you used the Astral Plane to travel to the plane you're currently wandering around on.
And this is where my question comes in - what about gate?
The DMG is pretty clear that other methods of planar travel, such as plane shift, don't provide the protection that astral projection does. I'm not going to go into whether a creature that can shift between planes innately possesses the same protections - that sounds more like a discussion than a straightforward question. I'm just interested in this one spell, and its implications. Normally, fiends, celestials and fey summoned to the Prime Material simply get sent back to their native plane upon destruction, and the only way to kill them permanently is to travel to their plane and end them there. Could you use gate instead to kill them permanently on the Prime Material Plane?