Two different actions
Delete from the library removes the item everywhere: out of every playlist it belonged to, off every screen showing it. One action, whole network.
Remove from a playlist takes it out of that rotation only. The item stays in the library and keeps playing in any other playlist it is part of.
Use the first when the content should be gone. Use the second when it should stop on some screens and continue on others.
How to delete
From Content, open the menu next to the item, choose Delete, and confirm.
Screens stop showing it on their next sync, which is usually within a few minutes. There is no need to visit each playlist first.
What deleting does not do
It does not remove the file from devices that already downloaded it. The player marks it as no longer needed and clears it during its next storage cleanup, which happens when space runs low rather than on a schedule. See Where content lives.
It also does not give you the file back. See Getting your content back.
Deletion cannot be undone, and we cannot restore a deleted file for you. Keep your originals in your own storage.