By way of yesterday's post in Functioning Form, I found Luke Wroblewski's 2005 piece A Difference of Design that takes a run at what makes "design thinking" different from the typical business approach to innovation. For example, he describes the problem solving approach between business and design as "definitive" (articulated proofs) v. "iterative" (modeling), respectively, which begins to answer the question I had about how design communicates. Iterative problem solving, happily, also corresponds to my preferred work method, "licorice on the saw."
He goes into more detail in the podcast Design by Design, which I have not yet listened to.
[starts] by looking at the cutting edges, the places where a classic design discipline -- say branding, architecture, or product design -- seemed to blur with something else. It is at the nexus of disciplines that the most exciting new developments tend to emerge.
Through example, it demonstrates how design is being used to tackle a range of problems from "saving us from our data," to doing digital manufacturing (MIT's phrase 'its from bits' sticks in my head), to creating buildings that breathe.