“Save to playlist” does what it says: it saves the tracks you’ve selected to a playlist.

“Save to library” will not save the selected tracks to a playlist. Instead it will save them to your cloud library and you’ll be able to see them by looking in Library -> Songs. Note that there is no specific order for “Songs” – you can sort them into whatever order you want.

Generally if you are not sure which you want, choose the Playlist option. If you later decide that you want to add them to your library this is easy to do after the event using the Music app itself.