Microsoft Visual Studio with Xamarin Extension
 Appropriate when you want to take advantage of a full IDE, like Visual Studio.
 You can visually design views with the iOS and Android, edit code with IntelliSense, and debug C# code in apps running in emulators or real devices.
 Take advantage of advanced Visual Studio features and your C# skills.

Xamarin Studio
 Appropriate when you want to use an IDE that works cross-platform on Mac OS X and Windows.
 You can visually design views with the iOS and Android, edit code with IntelliSense, and debug C# code in apps running in emulators or real devices.
 Take advantage of your C# skills.

Source Of Information : Microsoft Platform and Tools for Mobile App Development