Is MVC a Design Pattern or Architectural pattern
MVC is more of an architectural pattern, but not for complete application. MVC mostly relates to the UI / interaction layer of an application. You're still going to need business logic layer, maybe some service layer and data access layer. That is, if you're into n-tier approach.
Why does one of them have to be true?
Both can be true, depending on point of view.
MVC can be an architectual pattern, if it forms the basis of the application architecture.
It can also be seen as simply a design pattern, an abstract notion that is applicable to any application.