What is the difference between an overtone and a harmonic ?

Hint: Sound is a mechanical wave generated by the back-and-forth vibration of the particles in the medium through which it travels. As the energy of a sound wave travels through air from left to right, fragments of air can be displaced both rightward and leftward.

Complete answer:
Overtone: A normal frequency of vibration of an object is called a resonant frequency. A standing wave pattern is generated when something vibrates at a certain frequency. There are typically multiple frequencies at which this occurs for any given entity.The fundamental frequency, which is sometimes abbreviated as ${f_1}$, is the lowest of these frequencies.

Any resonant frequency above the fundamental frequency or fundamental tone is referred to as an overtone. The overtone sequence is a list of successive overtones for an entity. The first overtone in the sequence, as well as all subsequent overtones, may or may not be an integer multiple of the fundamental. Depending on the properties and geometry of the vibrating material, the relationship can be as simple as that, or it can be more complex.

Harmonic: Harmonic frequencies are whole-number multiples of the fundamental frequency, which is the lowest vibrational frequency. Take a look at a string that is vibrating. The vibration modes are all multiples of the fundamental and are proportional to string length and wave velocity. The relationship given below leads to higher frequencies being discovered.
\[{f_n} = n{f_1}\]
Wavelength: $\lambda = \dfrac{{2L}}{n}$ where $L$ is described as the length of the string.
The harmonic series is derived from this. The second harmonic, ${f_2}$, is equal to $2{f_1}$, and the third harmonic, ${f_3}$, is equal to $3{f_1}$, and so on. Also, for all values of n, the wave speed (the product of wavelength and frequency) is the same.

Note: In vibration, all harmonics may or may not be present, while all overtones are present. Both overtones are harmonics in this example with the loop, and all harmonics are overtones.