I would like to say that there is huge difference between the original short story "The Moon Pool", and its revised version that was included as the first part of the book The Moon Pool.
It is the original short story that Lovecraft read and hailed. It is a finely written piece of weird fiction. The revised version included in The Moon Pool book, is rougher and more pulpish, not as subtle.
Unfortunately I don't know where the original short story can be obtained, except in the original 1918 pulp magazine. And publishers don't seem to care to make the distinction. I found it in an online text (don't remember where), and xeroxed it onto paper.
It appears that the sequal, "The Conquest of the Moon Pool", was also revised, for inclusion as the second part of the The Moon Pool. But I have never read the original version! Does anyone know if it is available anywhere else but in those super rare earliest pulps?