There is a service organization in the United States, an offshoot of the Freemasons, called the Shriners. They typically raise money to help build hospitals for children born with birth defects and the like. They have adopted the fez as part of their uniform and the different lodge names reflect varied Arab and Egyptian themes.
If you free the tassel from it's "tassel broach", it's fun to swing around at parties.
I would describe Tatar male headgear as a short fez.