When you copy a playlist, you are essentially duplicating the playlist to your own list of playlists. You have the option to change the playlist’s name and also to edit the playlist by adding or deleting songs as you wish.
When you subscribe to a playlist, you are adding it your music library as is. You are unable to make changes/edits to the playlists you subscribe to. If the original playlist creator makes any changes to that playlist, you will be notified. You can access the list of your subscribed playlists by going to My Playlist (left menu bar) and then swiping left.