Hey geoffreyfromlexington,
Thanks for posting in Apple Support Communities. When you say iTunes subscription, are you referring to iTunes Match or Apple Music? That's an important distinction due to features of each. If you each have iTunes Match, that is likely expected since iTunes Match gives you the ability to sync all of your own music across devices. Check out Subscribe to iTunes Match - Apple Support for details. Your friend may be seeing the song in the iTunes Store if it is not in their library. From there, you can play a snippet before purchase.
If you are referring to Apple Music, make sure your friend is opening the Music app and not the iTunes Store for the reason mentioned above. Also, make sure you're using the following steps from How to share an Apple Music playlist on your iPhone or iPad - Apple Support.
"How to share a playlist on your Apple Music profile
If you have a profile on Apple Music, you can make a playlist public so anyone can find it when they search Apple Music.
- Open the Apple Music app.
- At the top of the Apple Music app, tap the photo icon
or your photo. - If you have a profile, tap View Profile. If you don't, tap Create a Profile.
- Tap Edit.
- Select the playlists that you want to share on your profile and in Apple Music search results. And deselect the playlists that you want to hide.
- Tap Done."
Take care.
