Apple have helpfullyₛₐᵣ꜀ₐₛₘ used the same word sync for copying files from your computer to a device over a cable (or local Wi-Fi) and using a cloud connection to update songs and playlists over the air when you have a subscription to Apple Music or iTunes Match. When syncing over a cable the app can only copy over files that are stored on local hardware and reachable at the location known to the library. Therefore any content that is not downloaded, or doesn't play when you try, cannot be copied. iOS devices on the other hand will normally show all of your unhidden purchase history in the cloud, plus any other content that you have added to your iCloud Music Library if you have a subscription. This can, perhaps, explain why it appears that purchases are being synced when they really aren't. Only locally stored media can be synced over a cable. Your computer needs to be authorized for any protected media, and content from the Apple Music subscription service must be downloaded directly to each device, it cannot be synced over a cable either.
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