So is it essentially identical (in this part) to the Google Music service. The first time you play a song it is streamed to your device and then recently played items are cached on the device along with any songs you select to keep on the device permanently?
Listen-while-download and streaming are two different things, although in some use cases this can effectively be a distinction without a difference. The Apple method downloads the music.
Yes, it caches it locally. #104 was observing that you can start playing what is in the process of being cached (assuming it’s getting the data faster than you can listen to it).
Apple’s breakthrough is being able to glance at the music on your PC, recognize that you’ve ripped CDs which are available on iTunes, and instead of making you upload the CDs you bought (which is redundant, as they already have a copy) just go ahead and download/cache the iTunes copy onto your iPhone. Google & Amazon would require you upload the CDs first, which for some of us could take _weeks_.
It looks pretty similar. The differences are that 1) iTunes in the cloud doesn't do streaming. 2) Google doesn't have a music store or agreements with the record labels, so you have to upload your files in their entirety; Apple recognizes music in its catalog and just stores a reference to it, so you don't have to upload.
I don't have an Android device, so there would be no point in requesting an invite; my assessment is based on Engadget's review. Note that Google's service is in beta, and we don't know what the pricing will be when it goes fully live.