I have Apple Music, why does iTunes still charge for songs?

I can search for a song/album and listen right away on my phone and ipad but iTunes wants me to buy the same albums to hear them?

All the featured albums are 'free' on my phone/ipad, the same featured albums on iTunes cost $

I thought with Apple Music it was all free with the subscription? And I could download any album/song with iTunes without paying for each one?

If that's not the case how do I get the albums I want that I downloaded for 'free' from my phone to my iTunes on my mac?

Thank you!