These quotes are from the book Engineering Design Methods: Strategies for Product Design, 3rd Edition, Wiley 2000 by Nigel Cross in Chapter 2 Design Ability. [note: I believe there is a 4th edition available now] Nigel explores the different ways designers and engineers approach and solve problems. He cites a number of studies, yet in summary, it appears there are two prevalent approaches.
The evidence from the experiments suggests that scientists problem-solve by analysis, whereas designers problems-solve by synthesis; scientist use ‘problem-focused strategies’ and designers use ‘solution-focused strategies’.
Engineers and scientists tend to systematically work to understand the problem. Based on this understanding then identify underlying rules and thus create an optimum solution. On the other hand, designers tend to initially explore the problem and propose a variety of possible solutions. They then work to find a solution that is satisfactory.