String stands for System.String and it is a .NET Framework type. string is an alias in the C# language for System.String. Both of them are compiled to System.String in IL (Intermediate Language), so there is no difference. Choose what you like and use that. If you code in C#, I'd prefer string as it's a C# type alias and well-known by C# programmers.
I can say the same about (int, System.Int32) etc..