AppleMusic playlists and sharing: can I only add songs I have bought?

I'd like to make a playlist of music I find on Apple Music, but somehow can't. I've got the idea that I have to buy songs before I can put them on playlist or share with my family, because I only can put on songs I have on my computer.

Can this really be the case? It seems useless to pay $15/month for being able to just browse music - I could just listen the songs for free on youtube, or buy them from Amazon without having to pay the additional $15/month. And if this is not the case, how do I add songs from albums I have not bought to my playlists?