String.IsNullOrEmpty or string.IsNullOrEmpty

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-know by C# programmers.

I can say the same about (int, System.Int32) etc..

They are the same.

Personally, I prefer to use String.IsNullOrEmpty. The alternative just doesn't look right. The same goes for choosing Int32.Parse(...) over int.Parse(...). And, of course, no matter what approach you choose, be consistent.

They are both the same.

string is a keyword alias in c# for System.String.

Only difference is that when using String, you need to use either System.String.IsNullOrEmpty or using System; at the begining of your code file.