I was recently informed my Bowler hat was in fact a Derby, now I always believed Bowler, Derby and its many other names Coke Hat, Boxer, Billy Cock, were all names for the same thing and for all useful purpose bar riding they still are.
The Bowler was first made and designed in 1850 by William Bowler for Sir William Coke for head protection when riding. The Derby got its name when the 12th Earl of Derby visited the United States in a hat of this style in 1880 and created a fashion there, so could be classed as the America name for Bowler.
Anyway if your looking for a difference a Bowler is hard and rigid, while the dome of the Derby Hat can be bent easily with the fingers, both are the same shape.
This hat is therefore a derby bowler.
All fashionable goblins (above) wear bowler hats as do steampunk man servants (below)