The reason behind the difference in sound roots from the difference in structure of both the musical instruments. The body of the cornet is mostly coiled, and is considerably shorter than that of trumpet. Some people also think that cornets are shorter versions of trumpets.
Another difference in both the instruments is that you will find more curves in cornets; trumpets on the other hand are longer and slender in shape. The shape of the bore in both the instruments is also different from each other. Even though both the instruments have cylindrical and conical bores, there is difference in the percentage of both. You will find two-third bore conical and one-third cylindrical in cornet. In trumpets, the situation is opposite; it has two-thirds cylindrical and one-third conicаl bore.
When it comes to harmonics, the cornet bore produces even harmonics while trumpet’s bore produces odd harmonics.