Im paying monthly for Apple Music but still being charged when I download a song

When subscribing to Apple Music, get your music from within the app (e.g. by searching the Apple Music catalog). The items there are not priced, as it is inclusive with the subscription.

When you get music from the iTunes Store, then you are buying elsewhere. The items are priced, and your purchases will be billed.

There are differences. E.g.: The music from the subscription can be added to your iCloud Music Library for the duration of the subscription. The music from the iTunes Store has a one time payment, and does not expire.