Industrial design (ID) education involves students with different cognition types. This study aims to explore and compare the design activities of problem-driven and solution-driven students and examine the stability of the design process of the two classifications regarding constraints. Based on the P-S index derived from Function-Behavior-Structure (FBS) ontology, 54 participants were classified into problem-driven and solution-driven classification. Design Issue, Syntactic Design Process, Process Transitions, and P-S index sequence of the two classifications were analyzed and compared. The results showed significant differences in these design activities between the two. Problem-driven students are inclined to constitute statements about the problem repeatedly rather than articulate the design details in the processes of design activity. Solution-driven students focus on the development of solution structure, and the intensity of generate solution is relatively high. It was found that the design cognitive classifications of ID students had relative stability during different experimental conditions. The constraint condition greatly increased the intensity of the design process of solution-driven students, but it was more complicated for the problem-driven students. The findings and results of this study would be useful for evaluating and understanding students' design activities, and it provides valuable insights and a basis into ID education and practice of different students' classifications.