Is a Flugelhorn a horn? Or a trumpet?

Why is a flugelhorn called a "horn" when it looks like a trumpet?  As with the English horn, it is thought that the name derives from use of "horn" as a generic term for instruments with many parts that widen into a conical shape. Coincidentally, "flugel" means "wing" in German, and it seems the name is derived from the shape of the instrument, which resembles a wing.
As the flugelhorn has many features in common with the trumpet such as its overall length and range, and the size of the rim and cup of the mouthpiece, there are many trumpeters who also play the instrument. For this reason, and as a result of its shape being adapted for easier use by trumpeters, the flugelhorn has taken on a form that now resembles the trumpet.