In the existing catalogues of either design patterns or architectural styles, numerous are very analogous. They show little differences because they have been developed and used by different people and for different applications. Therefore it is really very difficult, for practical use, to select the right pattern or style for a specific design problem. In general, the criteria given for selection are based on examples or case studies. The formalization of these patterns provides a criteria of comparison. In this paper, a context for style formalization that takes into account characteristic properties, is described first. Two styles, Mediator and Broker, are formalized. Then the relation of specialization is defined and applied to show that Broker is a particular case of Mediator. As an example, taking advantage of the distribution characterized by Broker, it is shown that in the PAC (Presentation-Abstraction-Control) architectural pattern, the usage of Broker as the control of the application, instead of Mediator, allows to define a distributed architecture for interactive applications, a distributed PAC style.