To design is to create something new. Design is not the same as problem solving in the mathematical or logical sense. Based on the actual menaing of the words problem and solving, problem solvimg implies that certain problems exist and that they are solvable. In most areas, ploblem solving also implies that it is possible to determine if a problem is solved or not. Most important, problem solving implies that a solution is either right or wrong.
However in design, there are no correct answers. Everyday design proposal is formulated in a close relationship with a changing and growing understanding of the situation (the problem). Since this is an on going process, it is never possible to determinewheather a design proposal is right or wrong. Still, we may note that a designer's current understanding of the designsituation is commonly referred to as athe "problem", and her ideas on how to proceed are called "Solutions."
The words mean different things in design that they do in formal logic, just to emphasize on it.