string is an alias for System.String. So technically, there is no difference. It's like int vs.System.Int32.
As far as guidelines, I think 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.
