The main difference between a C melody and a tenor saxophone is the pitch range and key they are tuned to play in.
The C melody saxophone was developed in the early 20th century as a transitional instrument between the traditional orchestral instruments and the emerging jazz band instruments. The C melody saxophone is pitched in the key of C, which means that when a C melody saxophone player reads a C on the sheet music, the note produced is a concert pitch C, unlike other saxophones, which are transposing instruments. The tenor saxophone, on the other hand, is typically pitched in the key of B-flat or occasionally E-flat.
Another key difference is that the C melody saxophone has a smaller bore and produces a brighter and more focused tone than the tenor saxophone. The C melody saxophone was also designed to be played with a different mouthpiece and reed setup than the tenor saxophone.
The C melody saxophone was popular in the 1910s and 1920s but fell out of favor due to its limited use in ensemble playing and the emergence of more specialized saxophones such as the tenor, alto, and soprano. Today, C melody saxophones are considered rare and collectors' items, while the tenor saxophone remains a popular instrument in many genres of music.