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1. TreeSet guarantees arrangement of elements according to their natural ordering always, HashSet doesn't guarantee.
2. TreeSet implements Red-Black Trees(spl Binary Tree, no arrays), while HashSet uses arrays and hashing mechanism.
3. For put, get, contains(), remove: HashSet - O(c), TreeSet - O(log n).

I guess TreeSet needs an ordering between elements, while a HashSet needs a mapping to some key.

EDIT: TreeSet uses TreeMap that implements RB Trees using Entry object with left, right nodes). HashSet implements HashMap...

TreeSet
- store set in a tree, sorted order of elements (increasing/decreasing) is preserved.
- insertion/removal/searching are O(log n)

HashSet
- store set in a hashmap, order of elements (whether sorted or insertion order) is lost
- insertion/removal/searching are O(1)

LinkedHashSet
- stores set in hashmap, plus a linked list to keep track of order of insertion
- insertion/removal/searching are O(1) , though extra space needed for the linked list
- order of insertion is preserved (due to linked list storing elements in order they are inerted)