They're probably referring to this photo [0]. This effect was actually due to the fact they were on the spacecraft in motion, but it's apparently possible to have an earthrise near the edges of the Earth-visible portion of the moon, because the Moon isn't completely stationary relative to earth:
> Because the Moon is tidally locked with the Earth, one side of the Moon always faces toward Earth. Interpretation of this fact would lead one to believe that the Earth's position is fixed on the lunar sky and no earthrises can occur; however, the Moon librates slightly, which causes the Earth to draw a Lissajous figure on the sky. This figure fits inside a rectangle 15°48' wide and 13°20' high (in angular dimensions), while the angular diameter of the Earth as seen from Moon is only about 2°. This means that earthrises are visible near the edge of the Earth-observable surface of the Moon (about 20% of the surface). Since a full libration cycle takes about 27 days, earthrises are very slow, and it takes about 48 hours for Earth to clear its diameter.
Kim Stanly Robinson also hits on this in Red Moon. Someone is emotionally invested in having a particular plot of moon where the earth peeks out through a gap in a crater wall during the wobble.
Sure, in the sense that the Earth can never leave a small fixed area of the sky, that area of the sky generally doesn't include the horizon, and the Earth cannot be seen to move at all except over very long periods of time.
In other words, not only are they not the same, they are not similar in any way, nor is "rise" an applicable term.
