Thanks for your reply.
Just to be clear,I am a subscriber to Apple Music and any music purchased through Apple is automatically sent to all of my devices. However, I have other music purchased through Amazon that are listed in my library on my iMac. Those are the items I want to add to my iphone 13. I tried to add them, but after I connected my iphone and opened the Music tab via the Finder, I found that the choice to sync only selected music,artists,videos,etc was chosen but gray (as in not active). I tried to sync anyway and got a message: Are you sure you want to remove existing music, movies, TV shows, and books from this iPhone and sync with this library? Of course, my answer is NO! I just want to add other items that are in my Music library on my Mac. What am I missing?