In practical terms, it's exactly like the browser version. In fact, it's just a WebView system that shows the pages the same. You can access your libraries, whether your music is from the online store or from your local files. The notifications show up on the bottom right corner of the Windows desktop, where you can access all the features.
There are also a few exclusive features in this version, like the option to transform it into a mini player that stays on top of other windows, letting you control the volume and skip between songs. There's also an exclusive options menu in the pop-up toolbar that lets you change the default theme color and mute notifications.