Why is my Apple Music Library not syncing properly?

I have Apple Music on both Mac Monterey and iPhone. Why doesn't the Library match up? I have more content on the Mac than on the iPhone. This aggrevates me because, in the car - my new acquisition being a 2021 Nissan Rogue - I would rather have a CD player. They cannot install one without uninstalling the factory installed navigation. Connection with smartphones interrupts, even when using USB cables. It limits me to AM radio news. Besides the Music content, I would like to know a better way to have a little music enjoyment in the car. The connections waste a lot of time before going off to my destinations. Thank you in advance.

[Re-Titled by Moderator]