Java: Hashset Vs TreeSet - when should I use over the other?

All I have been reading lots of blogs on this subject but still I could not get clear idea when to use one over another hashset or tree set.

Taken an example:

1. I have a comparable objects. I have put them in HashSet. Now when (only when I want) i want to set to be sorted based on compareTo logic, I can call Collections.sort(object)

2. whereas Treeset by default always use the compareTo or compare(obj1, obj2) all the time. Hence performance will be hit with TreeSet but output will be same as #1 (Collections.sort).

Is this understanding correct?

HashSet is Implemented using a hash table. Elements are not ordered. The add, remove, and contains methods have constant time complexity O(1).

TreeSet is implemented using a tree structure(red-black tree in algorithm book). The elements in a set are sorted, but the add, remove, and contains methods has time complexity O(log (n)). It offers several methods to deal with the ordered set like first(), last(), headSet(), tailSet(), etc.

1. First major difference between HashSet and TreeSet is performance. HashSet is faster than TreeSet and should be preferred choice if sorting of element is not required.

2. Second difference between HashSet and TreeSet is that HashSet allows null object but TreeSet doesn't allow null Object and throw NullPointerException, Why, because TreeSet uses compareTo() method to compare keys and compareTo() will throw java.lang.NullPointerException.

3. Another significant difference between HashSet and TreeSet is that , HashSet is backed by HashMap while TreeSet is backed by NavigableMap in Java.

4. One more difference between HashSet and TreeSet which is worth remembering is that HashSet uses equals() method to compare two object in Set and for detecting duplicates while TreeSet uses compareTo() method for same purpose. if equals() and compareTo() are not consistent, i.e. for two equal object equals should return true while compareTo() should return zero, than it will break contract of Set interface and will allow duplicates in Set implementations like TreeSet

5. Now most important difference between HashSet and TreeSet is ordering. HashSet doesn't guaranteed any order while TreeSet maintains objects in Sorted order defined by either Comparable or Comparator method in Java.

6. TreeSet does not allow to insert Heterogeneous objects. It will throw classCastException at Runtime if trying to add hetrogeneous objects, whereas HashSet allows hetrogeneous objects.