Is Google Play Music the same as the stock Android Music App? Is Google Play Music (formerly Google Music) the same app as the stock Android Music app?

I have a Nexus S running Android 2.3.6. I live in a country, Italy, where the Google Play Music service is not yet available. Some time ago, due to an Android Market glitch, then Google Music appeared among the apps installed on my phone.

The Market kept nagging me to update to the latest versions, which always failed because the app is not installed and I can't install it from the Market in my country. Before uninstalling the Google Play Music app entry, I'd like to make sure it's not the same as the stock Music app, which I instead want to keep.
No, it's a completely different service.

In fact, it's a cloud service with an Android app; whereas the Music app is simply a local music app.