As mentioned by others that you should upgrade to 1.1 of .NET framework to work with Visual Studio .NET 2003.
The coding in both the versions is same.
The differences between Visual Studio .NET 2002 and 2003 are:
1) Improved Intellisense and Code Completion Improvements
2) Debugging Improvements
3) Web Services Improvements which include WS-Security, WS-Routing, WS-Attachments, and DIME.
New Options available with Visual Studio .NET 2003
1) Development for Smart Devices
2) Development for Mobile Devices (Cell Phones)
When compared to Visual Studio.NET 2002, itís faster and more feature rich.
Actually, the WS* specifications (WS-Security, WS-Routing, etc) are not part of the .NET Framework v1.1 or Visual Studio .NET 2003. They are part of the Web Services Enhancements (WSE) package that you can download via MSDN.
As far as the differences between Visual Studio .NET 2002 and 2003, the biggest is the Framework version. I work with both versions relatively frequently (we maintain samples for both versions) and for ordinary use I don't see huge differences. If you're just looking at learning C# or programming with the .NET Framework, 2002 will work just fine. None of the basic syntax has changed and for the most part the libraries are all the same. If this were a commercial venture, though I would recommend moving to 2003.