Google Play, on the PC, is the Google Music cloud concept applied to the entirety of the Android Market (in this case, Music, Movies, and Books). It then rolls up the Android Market store, which... as far as apps are concerned, is simply a one-stop shop at that point. But in a desktop browser, it's more than the Market itself - it's a cloud-style home for everything not that doesn't entirely require the Android OS to utilize (and as mentioned above, then simply acts solely as a store for the apps/games that do require Android).
On Android itself, it's simply a rebadged Android Market. So far, it seems the separate Android apps (Music, Books, etc) still remain standalone, but have received the new Play label as well. 
I think this is the what the unified privacy policy is truly meant to bring about - unified Google services across as many platforms as possible (on the mobile front, likely only entirely integrated with Android, though some services available on WP and iOS). Eventually, Google+ will probably get more deeply integrated with these services (or the other way around?), and hopefully the recent surge in Google Drive speculation proves to be true - as that will probably be deeply integrated into everything-Google. Which, if it offers anything remotely approaching the storage capacity of Google Music (20,000 songs from personal upload, unlimited? Google Play purchases remain on the cloud/available for download/"pinning"), I will be a major fan, especially since SkyDrive, which could be so awesome, is completely relegated to browser-only on Android... at least OneNote and it's syncing capability is awesome on Android.