As far as policy goes, AA does not differentiate. Although AA.com calls them Emergency and Bereavement Fares, many agents still call them compassion fares. The end result, however, is still the same.

These fares are subject to availability and cost 1/2 the price of the full fare. The advantage of compassion/emergency/bereavement fares is that they are changeable, but they are not always the cheapest price. (Sometimes lower restricted fares are available for the desired flight.)