Usually "different" is used when there is a choice between two subjects, and "various" sounds more broad, and provides for choice among more than 2 subjects. Thus, "different" implies 2, while "various' implies several. Besides, "different" has another meaning - differing from.

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. :)