Correct
The bishop's hat has many names and variations. Some believe it is the same pepper with minor differences, others believe every pepper is different.
This is one of the reasons why this pepper called so many names such as Balloon, Pimenta Cambuci,Campane, Monks Cap, Chapeau de Farde, Peri Peri, Ubatuba Cambuci, Aji Flor, Christmas Bell and Bishops Crown or hat.
Now are they all the same pepper. For some such as TheChileMan.org
http://www.thechileman.org/results.php?chile=1&find=Bishop&heat=Any&origin=Any&genus=Any&subscribe=Search database, they are NOT the same pepper. SO it is possible that each one has its own unique shape, thus name.
However, They are all sharing some common features. All must be Baccatum, Not hot on the side, hot in the middle, has a hat, balloon, bell, cap..etc shape.
The one I have has really wide very sweet wings/sides