bool is an alias for Boolean. What aliases do is replace one string of text with another (like search/replace-all in notepad++), just before the code is compiled. Using one over the other has no effect at run-time.
In most other languages, one would be a primitive type and the other would be an object type (value type and reference type in C# jargon). C# does not give you the option of choosing between the two. When you want to call a static method defined in the Boolean class, it auto-magically treats Boolean as a reference type. If you create a new Boolean variable, it auto-magically treats it as a reference type (unless you use the Activator.CreateInstance method).