Basically: XNA Game Studios 3.0 and 3.1 come with Visual Studio 2008. (Note: anywhere I say "Visual Studio", this also applies to Visual C # Express.)
XNA Game Studio 4.0 (currently in beta) comes with Visual Studio 2010. (Note: XNA GS 4.0 is included with Windows Phone development tools).
Both Visual Studio and XNA Game Studio (and XNA runtime, for that matter) can be installed side by side with older / newer versions of the same.
XNA Game Studio (which basically means the content pipeline, clicking on the Xbox, project wizard, etc.) will only integrate with the corresponding version of Visual Studio.
Of course, you can reference any version of the XNA assembly from any version of Visual Studio. But without a content pipeline, this can be a bit restrictive.
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