Why is iTunes Charging On My Mac and not My Phone

On Macs, a single application (iTunes or Music, depending on the version of macOS you are running) provides access to purchased music in your library, to the Apple Music subscription service, and to the iTunes Store.

This is different from the arrangement on iPhones and iPads where the iTunes Store is in a separate app.

Perhaps the reason that your Mac is charging you for downloads is that you are looking at iTunes Store listings, rather than at Apple Music subscription ones. (It is possible to have an Apple Music subscription, and still buy individual songs or albums from the iTunes Store.)

Are both your iPhone and your Mac using the same Apple Account?