Object-oriented design is a method of design encompassing the process of object-oriented decomposition and a notation for depicting both logical and physical as well as static and dynamic models of the system under design.
As a noun, design is the named (although sometimes unnamable) structure or behavior of a system whose presence resolves or contributes to the resolution of a force or forces on that system. A design thus represents one point in a potential decision space. A design may be singular (representing a leaf decision) or it may be collective (representing a set of other decisions).
As a verb, design is the activity of making such decisions. Given a large set of forces, a relatively malleable set of materials, and a large landscape upon which to play, the resulting decision space may be large and complex. As such, there is a science associated with design (empirical analysis can point us to optimal regions or exact points in this design space) as well as an art (within the degrees of freedom that range beyond an empirical decision; there are opportunities for elegance, beauty, simplicity, novelty, and cleverness).
All architecture is design but not all design is architecture. Architecture represents the significant design decisions that shape a system, where significant is measured by cost of change.
In a quality object-oriented software system, you will find many classes that speak the language of the domain expert