We throw the word around so much without knowing what it actually means. Why are the physics based definition and the general definition of beats so different?
Colloquial beats and physics based definition of beats are not that different from each other!
In colloquial terms, beats are rhythmic repetition of sound.
In Physics' terms, beats arise the rhythmic rise and fall of the amplitude of the resultant when two waves of very similar frequencies interfere with each other. It arises from the addition of sines formula. i.e. \sin \omega_1 t + \sin \omega_2 t = 2 \sin \frac{\omega_1 + \omega_2}{2} t \cos \frac{\omega_1 - \omega_2}{2} t .
This shows that the amplitude of the resultant wave varies as \cos \frac{\omega_1 - \omega_2}{2} t . The beat frequency, therefore, is given by \frac{\omega_1 - \omega_2}{4 \pi} .
Read more about Physics based definition of beats at: https://byjus.com/physics/beats/