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This is what a solar eclipse looks like from the Moon
(thelemmy.club)
Captured by Firefly Aerospace’s Blue Ghost lunar lander on March 14, 2025.
The earth (one celestial body) is partially obscuring the sun (another celestial body) relative to the Blue Ghost lander (the designated observer).
It's an eclipse.
If you're on the earth it's an eclipse. On the moon nothing is between you and the sun, or you and the earth.
Put another way, an eclipse is only an eclipse from a certain observation point. For example, the crew of Integrity observed a solar eclipse on their way around the moon. The moon was between them and the sun. There was no eclipse for the rest of us on earth.
Check out Mr. Confidently Incorrect over here. An eclipse is exactly the definition you posted, I'm not sure how you could read it so wrong.