Changeling refers to both the Fae and mortal whose places were switched in infancy, so that the fae was raised as a human and the human as a Fae. This is a pretty rare thing nowadays, since the stealing of children is forbidden by Law. But, still, you might run into one some time in your life.

Halflings, on the other hand, happen when mortals and Fae breed. They exist in a sort of intermediate state - usually with mostly human looks and weak, Fae-like abilities - until they make a choice of which to become. The Choice has to be sincere and deeply desired by the Halfling to take place, and it doesn't always happen consciously. Those who become mortals tend to become particularly skilled at magic, and those who become Fae become whatever their Fae parent was.

Think of it this way: Changelings change places, and Halflings are half-and-half.