.NET 4.0 and earlier versions

string is an alias in C# for System.String.
So technically, there is no difference. It's like int vs. System.Int32.

As far as guidelines, it's generally recommended to use string any time you're referring to an object.

e.g.

string place = "world";

Likewise, I think it's generally recommended to use String if you need to refer specifically to the class.

e.g.

string greet = String.Format("Hello {0}!", place);

This is the style that Microsoft tends to use in their examples.

It appears that the guidance in this area may have changed, as StyleCop now enforces the use of the C# specific aliases.

LINQ to SQL only supports 1 to 1 mapping of database tables, views, sprocs and functions available in Microsoft SQL Server. It's a great API to use for quick data access construction to relatively well designed SQL Server databases. LINQ2SQL was first released with C# 3.0 and .Net Framework 3.5.

LINQ to Entities (ADO.Net Entity Framework) is an ORM (Object Relational Mapper) API which allows for a broad definition of object domain models and their relationships to many different ADO.Net data providers. As such, you can mix and match a number of different database vendors, application servers or protocols to design an aggregated mash-up of objects which are constructed from a variety of tables, sources, services, etc. ADO.Net Framework was released with the .Net Framework 3.5 SP1.

This is a good introductory article on MSDN: Introducing LINQ to Relational Data