Me neither (why they are still both there, it is still a bit confusing for new users))...

The connection strings are defined in the sqldataprovider class of your module

This code will read it from the first connectionstring (look at the HTML module source code for example):

        ' Read the attributes for this provider
         _connectionString = Config.GetConnectionString()

This code will read it from the second connectionstring (look at the the Survey module source for example):

            ' Read the attributes for this provider
            If objProvider.Attributes("connectionStringName") <> "" AndAlso _
            System.Configuration.ConfigurationManager.AppSettings(objProvider.Attributes("connectionStringName")) <> "" Then
                _connectionString = System.Configuration.ConfigurationManager.AppSettings(objProvider.Attributes("connectionStringName"))
            Else
                _connectionString = objProvider.Attributes("connectionString")
            End If

Hope this helps.