Can anyone kindly tell me which one should I install to develop database applications using C#?
SSDT or SQL Server 2008 R2? Or both are the same?
This two software are two different things, one is a Database Server (SQL Server 2008 R2) the other (SSDT) is a set of tools that expands functionality of Visual Studio to allow the developer to use a lot of feature that are in SSMS directly inside Visual Studio.
So you can install both .