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

/* 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);