I've never heard of different shades of gray being spelled differently. It's a concept I rather like, since I'm extremely color-sensitive and believe there should be more ways of differentiating between colors. But I don't think it's actually a real thing, sadly. At least, I've never heard of it in all my years as an artist and writer.
I'm going to chime in on the side of: "gray" is American, while "grey" is British. Unless you're talking about the name "Grey," in which case all bets are off. But yes, it's important to be consistent, not switching back and forth between spellings. As for which one to use, choose the spelling that agrees with your geographical location. If you're American, living in the US, and planning to submit your story to a US publisher, use "gray." If you're British, living in the UK, and planning to submit to a British publisher, use "grey."