Will the Astral Projection spell end upon entering an Outer Plane?

The astral projection spell states:

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 highlighted text seems to suggest that, when you enter a new plane via astral projection, your body is transported there as well and you may re-enter your body. This suggests you have lost your astral form and are now physical.

However, DMG 47 implies something different. This section talks about the astral projection spell for the purposes of traveling in the Astral Plane.

Astral Projection

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.

It further goes on to saying that high level adventurers will often prefer to travel to the Outer Planes via astral projection because dying in this form doesn’t mean “real” death.

So which is the right interpretation? Does astral projection put you back in your real body when entering an Outer Plane, thus ending the spell, or do you remain an astral projection?