The definition of problem solving can be different between researchers and regions of the world for various reasons. Frensch & Funke (2014) stated that:
researchers adopt definitions that they perceive as useful, that is, that are consistent with their beliefs, knowledge and theoretical goals. A definition can therefore be neither static, nor commonly accepted. Rather, for any domain of research, a number of meaningful definitions co-exist. In the area of problem-solving research, the current theoretical goals are different for North American and European researchers. The primary goal adopted by many North American researchers is to understand task performance and learning in natural knowledge domains. The primary goal adopted by many European researchers, in contrast, is to understand how people deal with complex, novel task situations. Because the theoretical goals differ for the two traditions, the definitions that have been adopted differ as well. Consequently, the two traditions are not concerned with the same phenomenon, and any comparison of research findings runs the risk of being meaningless.
Reasons for their statement is given in the whole section of the book (pages 13-19), which is readable via the Google Books website
In order to try to come up with an integrated definition, they came up with the definition of:
overcoming barriers between a given state and a desired goal state by means of behavioural and/or cognitive multistep activities (page 18).
Frensch, P. A., & Funke, J. (2014). Definitions of Problem Solving: The European Approach. In: Complex problem solving: The European perspective. New York: Psychology Press. pp. 13-19