Actually Microsoft .NET is not a operating system. Their new OS's are WindowsXP, also known as Whistler (for consumers) and Windows 2002 (for servers).

.NET is actually a just a specification for a framework. It is designed to allow developers (including msft) to create a set of services that are provided via a network architecture. Most portions of .NET will communicate over HTTP and use XML as a protocol. Microsoft is actually trying to sell .NET as a cross-platform technology.

Visual Studio .NET is a set of development tools to easily allow developers to create apps for .NET.

The bulk of Microsoft's development effort is not going into the .NET framework, but instead to .NETify it's existing products, which it is doing across the board. All of their new apps will use the .NET architecture, so you will see Office.NET, SQLServer.NET. It is actually a pretty good idea, there are similar solutions from Sun and IBM floating around.