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They are all variations of a theme. They all deliver the same music, at least for the most part, it just varies on how they serve it up and how much they charge for it. I think the main difference between Google Play Music All Access (and I agree, that really is a terrible name) and the others is that it is integrated into Android devices and the wider Google universe. On the other hand, services such as Spotify and Pandora have been doing this for a while now, and are pretty darn good at it with nicely refined UIs. Pandora in particular amazes me with how well it can pick music I like that I've never heard before.
"GPMAA" does allow you to upload your own library to the cloud and access it anytime, so it is different than the other services in that way. In essence it is a hybrid of a music storage and streaming music storefront. Nice feature.
I use Google Play Music, by the way, in addition to Pandora and Spotify, but I'm not going to pay $8 a month for the "all access" addition. At least not yet.
There is an article on Play Music vs. Spotify on IT World that you might like to check out.