Let's say there are many types of desserts - many individual slices of pie, cookies, cupcakes, etc. "You can eat anything you like" would imply I could have one, but it was entirely my choice which. "You can eat everything you like" is an invitation to have multiple items - two pieces of pie, several cookies, a cupcakes, etc.
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Hans51Sometimes "anything" and "everything" are interchangeable for the same meaning, aren't they?Yes, that's pretty much true. In many languages other than English, people say "everything" where we would say "anything" — as in your example.
Hans51Do you native English speakers feel any difference between them?Yes, but it
Hans51when a host says, "You can eat anything you want on the table", I could eat more than one food, right?Right. And you can eat more than one food if the host says, "You can eat everything you want on the table" (though it would be unusual for the host to say that).