The difference between web player and the desktop client is that you'll have to install the desktop client one to use and play music on it. It is a standalone program which will also have the highest amount of features.
The web player and browser player are pretty much synonyms to me, because both refer to open.spotify.com which can be accessed with an internet browser.
Edit: There's now an official statement on Twitter (@SpotifyStatus) notifying that they are aware of the issues and are looking into it. I suggest keeping your eye on SpotifyStatus for further tweets. :)
Feel free to ask more questions :)
SebastyRock Star 16
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