Both the GridView and DropdownList server controls provided in ASP.NET have DataSource and DataBind methods. This means that you could write the same code to populate both controls with data from a database. So first you would create a method for a class like this:

public DataTable GetData()
{
string strSQL = "select * from tblTest";
using(SqlConnection myConn = new SqlConnection(ConfigurationManager.ConnectionStrings["MyDB"].ToString()))
{
    using(SqlCommand myCmd = new SqlCommand(strSQL, myConn))
    {
           myConn.Open();
           using(SqlDataReader myReader = myCmd.ExecuteReader())
           {
                 DataTable myTable = new DataTable();
                 myTable.Load(myTable);
                 myConn.Close();
                 return myTable;
           }
    }
}
}

And then in the codebehind for the page that contains the GridView or DropDownList controls you create a new instance of the class you created above and set the DataSource property for the control. So if you created a class called myClass your code for the Gridview would look like this:

        myTestClass myClass = new myTestClass();
        gvMyGrid.DataSource = myClass.GetData();
        gvMyGrid.DataBind();

The only difference for the DropDownList would be setting the DataTextField and the DataValueField.