if you join apple music are the songs free to download or are they still billed?

Having a subscription does not in any way preclude you from buying a song.

Make sure when downloading a song, you are in the correct section. The iTunes Store section in iTunes on a computer, and the iTunes Store App on an iOS device will let you buy a song outright to keep and continue to play even if you discontinue the Apple Music service. You have to pay for these purchases.

To get songs from the Apple Music service, make sure you are using the Browse or For You sections in iTunes on a computer, or in the Music App (not the iTunes store app) on the iOS device.

When done right, you will not see a price tag associated with the song, and can download it through the Apple Music subscription service.

Add and download music, shows, and movies from the Apple Music catalog - Apple Support

They charged you if you purchased it. The Apple Music subscription allows you to listen online, and to download to the device for listening offline (you can't transfer a downloaded file to another device); as said above, if you stop the subscription you can't go on playing anything you've downloaded. If you purchase a song, as you appear to have done, you can keep it indefinitely independently of the Apple Music subscription. Your 'purchased items' listing in the Account details in the iTunes Store will confirm what has happened.

They’re free with the subscription, but won’t play if you discontinue it.

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Apple charged me for a song on iTunes. I have the same question. Why am I being charged? I am paying for a monthly subscription of Apple Music.

I use a PC, iPhone and a Laptop.