They are mostly the same, but a little different.
Different means there is something about two or more things that is not the same, and brings attention to that. Various describes a diverse group of things, and brings attention to the amount of things that are different, not just that "none of them are the same," it's more like "there are a lot of different types."
I'm not sure if this is the same for all uses, but I hope it helps. :)