In the backstage videos of music videos, you can see that camera operators are filming with small video cameras.
In the backstage scenes of TV shows, you can see that cameramen are filming with large cameras that they carry on their shoulder (or mounted on a tripod).
Comparing the quality of music videos and recordings of various shows posted on YouTube by TV channels, I do not find any difference.
It seems that small video cameras shoot just as well as large video cameras.
What is the difference?
This video answers your exact question: https://youtu.be/RkTaMyatsTo?si=1JaqDosk-5Xuu1y1 It just seems to be a very flexible option where you can record stuff that is very close or very far away.