System.Data.SqlClient
is the .NET Framework Data Provider for SQL Server. ie .NET library for SQL Server.
I don't know where providerName=SqlServer
comes from. Could you be getting this confused with the provider keyword in your connection string? (I know I was :) )
In the web.config you should have the System.Data.SqlClient
as the value of the providerName attribute. It is the .NET Framework Data Provider you are using.
<connectionStrings>
<add
name="LocalSqlServer"
connectionString="data source=.\SQLEXPRESS;Integrated Security=SSPI;AttachDBFilename=|DataDirectory|aspnetdb.mdf;User Instance=true"
providerName="System.Data.SqlClient"
/>
</connectionStrings>
See http://msdn.microsoft.com/en-US/library/htw9h4z3(v=VS.80).aspx