The difference between "varied" and "various" is that with "various, you're referring to a lot of something. For example, if there are a lot of cars in the parking lot, you can say "There are various cars here." With "varied" it means there is different forms of one particular object. Like you mentioned with the menu, it is "varied" because there is a lot that you can choose from. Here are some examples just in case these rather general definitions didn't help: There are various answers to this question. Various people wanted to help me today!! The varied weather in this city can never make up its mind; it's always changing!! This list is quite varied as there are people from different parts of the world in it. Hope this kind of helped.