When you sign into your Apple ID on any computer or device you get access to your unhidden purchase history in the cloud. If you have iTunes Match or Apple Music you also get access to your iCloud Music Library which can include additional songs that have been matched or uploaded from a computer or device, or in the case of Apple Music, other songs from the iTunes catalogue that you choose to add to your library. This library can be shared across up to ten computers and devices, all of which will have access to the same collection of tracks and playlists. A change made in one location should be reflected in another via the cloud. If you have Sync Library or iCloud Music Library enabled on a computer then you will see the entire iCloud Music Library, along with any ineligible content in the local library or any other content that hasn't been added to the cloud library. By definition this content will only be stored locally on that computer.
I referred you to Identify cloud status icons in your music library on your Mac or PC - Apple Support earlier so that you can check on the status of tracks in your library. The notification you posted earlier states that the playlist Christmas will be removed from the iCloud Music Library if you proceed, but you haven't told us anything about the song or songs you were trying to add to it at the time. Removing a playlist doesn't of itself remove any tracks from the library. I don't know it the playlist already contains some items. The only thing I can tell from here is that one of the tracks you were trying to add is in your local library and ineligible for iCloud Music Library, otherwise you wouldn't have got that warning message. Closely inspect the tracks you were planning to add to see if you can work out which was causing the issue and why. One possible cause might be a locally stored track bought with a different Apple ID.
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