I've been thinking about this concept for some time...and don't know if I've yet fully formed the thoughts. Maybe this will be more of a "thinking out loud" exercise. And Doug's comments help frame the discussion.
Redefining words to mean what we want them to mean seems to be in vogue these days. So, I'll provide my own definitions. I don't think that they're that far off from the "official" meanings. First, style. For the sake of this discussion,
style is the "decoration" applied to design. Design would be the arrangement of the elements to accomplish the intent. These might be a bit awkward...so I'll give an example from a different field. In music, we have many styles...rock, jazz, country, western, blues, classical (with its many sub categories), etc. These are independent styles of music. Within each style there are an infinite number of compositions, or "designs." The "design" is related to the style, but in many ways independent. Or, better put, the style provides a framework for the design.
Using the example above, a design is dependent upon the style its derived from. You could also have a lack of style (I don't mean bad taste, but being void of style) and still have a design.
I think that one of the problems we have with residential architecture is that style has been divorced from design. Things are designed without an understanding of the rules imposed by a particular style.
Before I go to far with that idea, I want to discuss that some styles impose strict design rules. Classical proportioning systems are very particular about how things work. New England Colonial architecture has certain design elements that are required by the styles. A southwestern adobe house has different arrangements than a center hall colonial. These design rules are typically driven by the climate and geography of the land where the style originated.
What styles are currently popular? Arts & Crafts, Prairie, "traditional" (a word that seems to have no real meaning), craftsman. These are the types of houses that people seem to want. If we look at the original structures designed in these styles, we'll see that they have common architectural elements...and these are more than just the "decorative" elements. Plan and function are important to these designs. When somebody wants an "arts & crafts" house today, there is little thought to what that means. Is that a craftsman bungalow? If so, which sub-type?
But I don't think we can be too picky... I think one of the things post-post-modern architecture has given us is the ability to think through the design on more than a superficial level. As Doug pointed out, our house was designed to reinforce certain living patterns and create new ones. So far, it appears to be successful at this. But the "style" of design I chose for didn't really exist. The lot precluded certain common formal arrangments. I knew the feeling I wanted was a "Scandinavian modern." What's that? Something I've made up. It's a my mix of Alvar Aalto, Eero Saarinen, what I remember I liked when I lived in Finland and the influnce of my father (and to a lesser degree my mother). It's a "modern" sensiblity with the warmth of Wright. The style was made up out of whole cloth. In this case, the style was created to match the design. I could have trimmed it out in a more "traditional" way...dressed it up with elements that might have evoked a different feel, something more like our neighbor's house. We can dress up designs that work for today with just about any style.
So, we've turned the rule upside down...or maybe is an associative rule (A=B and B=A). The design was a framework for the style to be worked out.
So there it is...style is not design and design is not style, but they are related and need to be considered in light of each other.