There isn't a difference, although it would make more sense to say "Can I get one of everything?" if you are ordering food at a restaurant and want to try one of every item. "Can I get each of everything?" doesn't really sound right.
@hjobk Sorry for the late response. I wouldn't say that it's grammatically incorrect, I just don't really hear people say that. It would just be more common to say "Can I get one of everything?" The word "each" is used to refer to one part of a group. Some examples would be "They each have an apple." or say you are at a bakery and they have 3 different kinds of croissants. You want to try all 3. You would ask "Can I get one of each?" or like you said, "Can I get one of everything?" would also be okay. I honestly couldn't tell you if "Can I get each of everything?" is actually incorrect, in my opinion, it just isn't a very common way to ask for one of each of something.
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