We use the term design to describe the qualitative nature of a scheme, in contrast to scope that describes it quantitatively.
An extension may provide say 35 square metres of open plan living space, with kitchen, dining and sitting zones (the scope). The same space might create a lofty and spacious feel, from materials with natural grains and textures, be laid out to maximise efficiency and elegance of the plan, to perform to a very high environmental standard that is comfortable year-round with minimal heating/cooling requirements, and to make use of creative storage solutions in order to preserve a clean and decluttered appearance (the design).
Think of Scope as the noun and Design as the adjective that adds quality and brings it to life. Typical design attributes might include the following:
Aesthetics, the look, feel and experience of the architecture.
The function and performance of the architecture.
The application of innovative and creative solutions to the architecture.