The Cornet is related to the trumpet, but it the compact British version frequently used in the Salvation Army brass bands. All the 'valveings' are the same as the trumpet, but the cornet produces a mellower sound, and according to some, is easier to learn, although that's all in the mouthpiece.
The cornet, like the flugelhorn, is a trumpet relative, but with a larger, conical bore. This instrument also has a slightly deeper mouthpiece than that of a trumpet, having a conical bore. The french horn and flugelhorn also have this. The larger bore produces a warmer, more horn-like tone, similarly to that of the flugelhorn. It can also have third and/or first valve triggers or loops, so that the player can "kick the slide" to get certain notes in tune, namely low D and C#.