Hello christopherfromstanmore,
Thanks for posting. As I understand it, you're finding that songs downloaded when played on your Mac, and you want to know if you can play songs on your Mac without downloading them.
This covers how you can Play songs in Music on Mac. Are you referring to content from Apple Music specifically, or iTunes Store purchases? I tested this on my Mac and I am able to play iTunes Store purchases without downloading by double-clicking the track.
Try opening the Music app and clicking Music > Preferences > General. You might try unchecking "Automatic Downloads" and "Always check for available downloads" to see if either helps.
Best wishes.