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Extended stored procedure is a special function packaged in a DLL. Extended stored procedures for SQL Server can be written either in C/C++ or Delphi (Since SQL Server 2005 it is possible to create extended stored procedures in C#). Like regular T-SQL stored procedures (or .NET extended stored procedures for SQL Server 2005 and later), they can accept input/output parameters and produce recordsets. And yes, all the WinAPI can be used there.

The significant difference between a regular T-SQL stored procedure and an extended stored procedure is that the latter allows variable list of input parameters of different datatypes!
So, the actual number of parameters and their datatypes can be determined by an extended stored procedure at runtime.