when to use Set vs. Collection?

Is there any practical difference between a Set and Collection in Java, besides the fact that a Collection can include the same element twice? They have the same methods.

(For example, does Set give me more options to use libraries which accept Sets but not Collections?)

edit: I can think of at least 5 different situations to judge this question. Can anyone else come up with more? I want to make sure I understand the subtleties here.

1. designing a method which accepts an argument of Set or Collection. Collection is more general and accepts more possibilities of input. (if I'm designing a specific class or interface, I'm being nicer to my consumers and stricter on my subclassers/implementers if I use Collection.)
2. designing a method which returns a Set or Collection. Set offers more guarantees than Collection (even if it's just the guarantee not to include one element twice). (if I'm designing a specific class or interface, I'm being nicer to my consumers and stricter on my subclassers/implementers if I use Set.)
3. designing a class that implements the interface Set or Collection. Similar issues as #2. Users of my class/interface get more guarantees, subclassers/implementers have more responsibility.
4. designing an interface that extends the interface Set or Collection. Very similar to #3.
5. writing code that uses a Set or Collection. Here I might as well use Set; the only reasons for me to use Collection is if I get back a Collection from someone else's code, or if I have to handle a collection that contains duplicates.