How much divergence would be needed for classifications as astrobiology?
I think if life was transferred to either body on a probe, it would not count as alien yet because it could not have had time to develop very far on its own, since all probes are recent evolution wise. These would be offshoots from earth life. Truly alien life would most likely use different biochemistry because it originated in a different planet, it would be a totally different tree of life. However, the presence of life on the moon or mars, even if just contaminating earth bacteria, would be incredibly important for astrobiologists, as it would provide direct evidence that life can survive in these harsh environments. Life on the moon would most likely be dormant bacteria, because there is no air or water or food. However, if bacteria could survive prolonged exposure to space and be revived upon entering a suitable environment, that would provide evidence for panspermia. Read this: https://en.wikipedia.org/wiki/Surveyor_3

If panspermia is true, then those aliens might not be that unrelated after all. But until we find one, we can't make any conclusions.