The know-how is knowledge of the ways in which the accomplishment of a task. The equivalent English term know-how is used quite regularly, without particular utility in the technical and economic literature.
The expertise is different from other knowledge such as scientific knowledge because it can be applied directly to a task. Expertise in problem solving is different from knowledge on solving problems. For example, in some legal systems, the expertise is considered intellectual property of the company, and can be transferred when the company is acquired.
One advantage of the expertise is that it can involve more dimensions, such as hands-on experience, training in problem solving, understanding the limitations of a specific solution, etc. Thus, the expertise can frequently eclipse theory.