In this day and age where it is "cool" to wear funny hats, I see a lot of bowlers. As you know, a bowler is a type of hat that has a wide brim and a dome-shaped crest: you know, the type of hat stereotypically worn by bankers and short James Bond villians. I also see people who wear hats they like to call "derbys".
Now, these hats look exactly alike, but their wearers proclaim that bowlers and derbys are actually different styles of hat. When asked to explain themselves, I hear wild excuses such as: "A bowler has a band around the dome," "A derby has a wider brim," or (my personal favorite) "One is rounder than the other."
Actually, derbys and bowlers are the same type of hat!
The derby was made popular by the 19th-century Earl of Derby (pronounced "darby"), but it was known as a bowler. When the hat came to America, the Americans, being the random sort of people we are, decided to call the hat a derby, after the Earl. However, because Americans tend to slaughter language, the pronounciation became "durby". Later, we reverted to Britain's name of "bowler", and that is what the hat is most commonly called. However, due to the time where "derby" was the norm, there are still people who hear the name "derby" and use it. Anybody who tells you the two hats are distinct varieties of hat is wrong.
So, pick the name you like best, and go with it! Just remember, your hat has multiple names.