The photo in which a reflection of Neil Armstrong is visible in the visor of Buzz Aldrin is a photo of Buzz Aldrin. It's not a photo of Neil Armstrong, it's a photo of Buzz Aldrin that contains a very small reflection of Neil Armstrong in Aldrin's visor. Aldrin takes up around 700X as much area in the photograph as Armstrong's reflection does. It's a photo of Buzz Aldrin!
That's how the author of the photo, Neil Armstrong, described it.
Until 1987, when it was conclusively established that the photo Christie's describes as The Only Photo of Neil Armstrong on the Moon contains a full bodied image of Neil Armstrong, he often stated unequivocally that none of the photos taken during his EVA on the Moon's surface were of himself. This demonstrates that Neil Armstrong himself did not consider the photo he took of Buzz Aldrin that included a small reflection of himself while taking the photo to be a photo of Neil Armstrong.
Here's a 70mm (film format) photo taken with one of the customized Hasselblad 500C cameras used by the Apollo crews of Neil Armstrong on the Moon:
Half resolution version of the original as released by NASA due to file size limits here at SE
He's resting inside the LEM after his and Buzz Aldrin's historic moonwalk. He appears to be both elated and exhausted after making history in a way no other person ever has. The LEM is still parked on the Moon's surface. Just as a pilot sitting in an airplane on a taxiway is said to be "sitting on the tarmac" while awaiting takeoff, Armstrong is "sitting on the Moon" inside the LEM.
Here's a cropped and exposure corrected version released by NASA:
One-quarter resolution of the original released by NASA due to size limits here at SE
Here's a single frame from a 16mm timelapse movie that was taken by Buzz Aldrin from inside the LEM at the beginning of Armstrong's moonwalk before Aldrin also emerged from the LEM and joined Neil outside.
This is a frame grab from the television camera mounted on one of the LEM's lander legs that beamed a live signal back to Earth as Armstrong descended the ladder before setting foot on the moon for the first time in human history:
There's at least one other photo that shows a silhouette of Armstrong's helmet and part of his right shoulder in the deep shadow under the LEM in the far corner of a photo taken by Aldrin to document an equipment bay on the LEM's landing stage. It wasn't established that this poto contained part of Armstrong's spacesuit until in the mid-1990s.
And of course, this is probably the most recognizable photograph in the history of the human race:
The full image from which a very small portion was cropped and included in the question
One can see a reflection of Neil Armstrong taking Buzz Aldrin's photo, along with parts of the LEM and some of the other scientific items they've placed on the Moon's surface around the LEM at Tranquility Base, on the front of Colonel Aldrin's face shield.
This photo was taken by Neil Armstrong. Armstrong had seen prints of it since almost immediately after his return to Earth at the end of the Apollo 11 mission. Yet he often stated from that time until 1987 that there were no photos taken of him during his EVA on the Moon's surface.
But that's neither here nor there.
- The photo is described by Christie's as "The only photograph of Neil Armstrong on the Moon" has been referred to in this way since 1987.
- The fuller description of the photo was "the only 70mm full body photograph of Neil Armstrong on the Moon." 70mm describes the film format size used by the customized version of the Hasselblad 500C cameras used on the Apollo 11 moonwalk.
- When anyone familiar with the history of the Apollo program hears the expression "the only photograph of Neil Armstrong on the Moon" they know exactly which photograph is being referenced.
- The very limited number of other photos of Neil Armstrong taken during his EVA on the Moon's surfaces are either reflections off of other objects, video or movie frame grabs, or captures of small parts of his spacesuit in deep shadows that would not be identifiable at all except for the fact that the only other human being within range of the camera's resolution limits was the photographer, Buzz Aldrin. They're not photos of Neil Armstrong in the way that most folks would understand a description of a photo that says it is a photo of someone.
So is this photo the only photograph that contains an image of Neil Armstrong on the surface of the Moon?
But it is the singular photograph that has been titled for over thirty years as:
"The Only Photograph of Neil Armstrong on the Moon"