According to Canon, this is the third generation (hence G-III) of the Canonet series (I'd argue that it's the fourth: there's the original Canonet, the QL series and the New Canonet series). Unlike the New Canonets, it's easy to spot these because there's a G-III badge on the side of the body next to the lens.
The Canon Camera Museum says the "G" stands for "Grade Up." The "grade up" simply means that it's a 17-L: you get in-viewfinder battery check. Woo hoo. Still, this is probably the most valuable of the Canonets. It tends to fetch the best prices. The G-III series would mean it was built later and hopefully less likely to be worn or broken. But if you want to actually use the camera, you can save some bucks and get the New Canonet 17, or a 17-L if you want battery check. It's the same camera. But also note that these cameras run on 1.35v mercury cells which can't be had anymore. If you want to use the built-in metering, you need to work with modern 1.5v battery "equivalents" and make adjustments for it.
Canon also released the G-III 19, which is identical to the New Canonet 19. And the only difference between this and the G-III 17 is that the 19 has a slightly smaller aperture on a 45mm lens, whereas the 17 is a 40mm lens. And there's no battery check.
This is the last of the Canonets. Canon retired the name when they launched the all-new, truly automatic Sure-Shot series, beginning with the AF35 and AF35M.