Ron,
I had the same thought as you. I guess that the carving artist had not developed his skills to where he could correctly depict an eagle
Tac,
Tom is correct. The term Bar-B-Que Gun originated with the Texas Rangers & early Texas lawmen. Those that could afford them owned a "working gun' and a "fancy gun". They wore their working guns everyday on the job. When they had to make a court appearance, attend a social function, public bar-b-q (cook out), etc, they "dressed up" by wearing their fancy guns and tooled leather holsters. These became known as Bar-B-Q guns. Sometimes the competition grew fierce as to who could wear the fanciest gun & rig.
Here are a few more examples for your viewing pleasure: