Music I download from Google Play isn't showing up in Music Play?

[Grifftech2K13]

They show up in Google Play Music app (the Headphone icon) But I don't see them on the Music Play app that came on the phone Its a round Blue icon with a green note on it. I wish I could have just one app on here and stop bothering with it. Can anyone help?

Thanks,
Chris

 

[Grifftech2K13]

Also I want all my music on the phone and I dont want to stream it like the Google Play Music App does.