Try reading my profile; I didn't know this was settled: http://www.windows.ucar.edu/tour/link=/earth/moon/moon_evolution_overview.html
Well, that took a while. I hadn't noticed that you had misspelled professor in your screen name. Obviously I wouldn't have thought that you were really a professor, if I had noticed that sooner.
I didn't know this was settled:
I followed your "earth/moon" link. It reminded me of the books on cosmology, written for kids, that I read in the '60s. I was exposed to a much more complete picture when I went to CalTech, in the '70s.
Suffice it to say that the "capture" theory is just silly.
The third case is generally accepted as fact. The first case could simply be a way of looking at the third case, depending on how the terms are defined.
There is geological/selenological evidence that the Earth and moon (Luna) are linked. They formed from essentially the same material, at essentially the same time.
There is also a geological record of the change in the Earth's rotation rate. Legend has it that Isaac Newton explained the linkage of the Earth's tides, the widening orbit of the moon, and the slowing of Earth's rotation, when he was 12 years old.
I don't know if the legend is true, but I learned about it as part of a cautionary tale about asking stupid questions of Richard Feynman. I was 18 at the time, and promptly figured it out for myself. Any CalTech freshman could have done the same.