What is a different in a french horn and a brass instrument?

The only differences are the size, the french horn mouthpiece is smaller, and the instrument they were made for!

French horn mouthpieces are conical producing a warm round sound, whereas Trumpet mouthpieces are cup shaped which allows for a brighter more direct sound. The rim (where the lips touch the mouthpiece) of a horn mouthpiece is generally narrower and much thinner than a trumpet mouthpiece.