[curiousuburb]

IIRC, some of the compositional analysis of Moon rocks that helped confirm historical origin yet Lunar uniqueness was the particular balance of other rare radioactive isotopes. Bombardment by cosmic rays on the Moon causes further changes (some of which allow us to confirm they're not recently of Earth), but the 'fingerprinting' is primarily isotopic concentrations. Martian meteorites are also distinct due to their own isotopic fingerprint.

As for the actual process by which the Moon was fractured off the early Earth, there are some NASA simulations of this done with varying degrees of particle dynamics and physics precision over the years. Some astronomy software (Starry Night, IIRC) also includes animations of this event in their multimedia gallery on CD/DVD.