Differentiating music versus regular noise is ultimately subjective. However, reading brain signals confirms that we do perceive them differently, but just what makes a music stimulus different from a "noise" stimulus? An article by Reybrouck et al. published in 2019 found three main differences:
Sounds that are extremely loud, even if originally created as music, are more often perceived as "noise". This includes any sound which could potentially inflict deafness. However, some people have a personal preference for much louder music, though obviously they can only listen to it to a limited amount of time before going deaf. To be perceived as music, sound must be within an acceptable decibel range. Generally, music at 60-70 decibels is ideal, as well as anything lower - anything higher may just be perceived as noise.
2. Sounds that are simply unwanted are more often perceived as noise. This doesn't necessarily mean that music is always wanted, or that the sound is bad, just that it is not what we are listening for. Some examples might include a lawnmower, the humming of AC, or the scribbling of pencils in class.
3. Sounds that are extremely random are more often perceived as noise, while music is generally more organized (though this varies widely by culture and genre of music).
This TED-Ed video is an excellent explanation of some differences between noise and music. It highlights that music is an art form, and the line between noise and music is often blurred in pursuit of different audience reactions.
References
Hearing Health Foundation. (2023). Keep Listening | What Are Safe Decibels? Hearing Health Foundation. https://hearinghealthfoundation.org/keeplistening/decibels
Reybrouck, M., Podlipniak, P., & Welch, D. (2019). Music and Noise: Same or Different? What Our Body Tells Us. Frontiers in Psychology, 10(1153). https://doi.org/10.3389/fpsyg.2019.01153