All harmonics are overtones - QS Study
QS Study

In a sample of musical note the tone, which have minimum frequency is called fundamental tone. Except the fundamental tone all other tones are called overtones. The overtones which have frequencies as the simple integral multiple of fundamental tone are called harmonics.

So from the definitions of fundamental tone, overtones and harmonics, it is proved that all harmonics are overtones but all overtones are not harmonics.