Apple Music (especially when coming from iTunes) has a very tight concept of a "Library". If you add an album to your library, all the songs are also in your library. If you add a playlist, you have the option to add all the songs to your library.
In my (arguably limited) experience with Spotify Premium, I can't browse all my songs in my "Library". If I'm missing something in the UI, please let me know; I would love to hear otherwise.