I am not the best at describing things, but I will try my best. Shine is when light is reflected off of an object, like 'A metal object may shine in the sun.' A glow is when something makes its own light, like 'A light bulb glows so brightly you can't look at it without hurting your eyes.'

I think Wings has given a good answer, even though we say "the sun shines" (maybe it's an exception?). Perhaps the main feature of something that shines is that it is very bright, and the main feature of something that glows is that the light is steady.