The term overtone is used to refer to any resonant frequency above the fundamental frequency - an overtone may or may not be a harmonic. Many of the instruments of the orchestra, those utilizing strings or air columns , produce the fundamental frequency and harmonics. Their overtones can be said to be harmonic. Other sound sources such as the membranes or other percussive sources may have resonant frequencies which are not whole number multiples of their fundamental frequencies. They are said to have non-harmonic overtones.
All harmonics are overtones for an open air column or a string .
Closed air columns produce only odd harmonics. A rectangular membrane produces harmonics, but also some other overtones.