It appears that almost no one plays cornet, just trumpet. I can't hear the difference. What's the deal?
What is different about the pro models, which cost substantially more?
Are there new mouthpiece designs which make it easier to hit high notes?
The trumpet and cornet are cousins to each other in the brass family.
A cornet has a conical bore, meaning the tubing gradually gets wider over the length of the instruments. It typically has a mellower sound compared to the student trumpet. They’re not as commonly used today, but were popular prior to 1970 or so for use in school bands. Some of the great classic solo literature was specifically written for cornet, such as the works and arrangements of Herbert Clarke. Most are in the key of B-flat.
The trumpet has a cylindrical bore, where the tubing is a consistent diameter (until the bell flare). It has a considerably brighter sound than the cornet, and projects much easier. Composers like Mozart and Beethoven usually wrote for two trumpets in their symphonies, which often played in octaves and doubled the timpani. They didn’t have valves in those days, which limited how many notes could be played. Trumpets are also widely used in jazz music, and can easily project through a full-sized jazz band. Most are in B-flat (band/jazz) or C (orchestra), but are available in other keys as well.
The bugle, like the cornet, is usually conical. It has no valves, so it can only play notes of a single overtone series (usually in the key of G). They’re still used in certain military functions, as well as the Boy Scouts. Bugle calls were used to transmit orders in battle before modern inventions such as radio.
Primarily, it is a matter of tradition. Cornet tradition and trumpet tradition. Professor Stephen Thomson provides interesting insights into this through Schlossberg's work.