Sent from my LG-LS970 using XDA Free mobile app
Gee ROMS can be used on almost any variant of the Optimus G, but basically it's a compatible source tree for GEEspr and GEEhrc which are respectively sprint ls970 and the international e975.
Also, the GEE roms can be used on the ATT version with a compatible kernel. There have been a lot of questions about it but basically the sources for GEE are newer than the sources for the ls970 which would be what you see as gproj.
The GEE sources are really compatible and depending on the ROM there are little to no issues and you won't notice a difference to the naked eye. When flashing a GEE ROM make sure to use a GEE kernel, there are only 2 kernels for the gproj source, so anything you see with ls970 that does not say GEE will only let you use one of those 2 (maybe 3) kernels.
Some phones work better with one or the other but I have never had a problem with either.
Keep browsing and I am sure you will find a more direct answer, but this is my experiences with it as I too was one with questions.