Existing studies on Massive Open Online Courses (MOOCs) examine learners' engagement processes but have not explored links between them and motivations to enroll. In our previous work, we identified intrinsic, professional, and prosocial motivations for taking MOOCs. In this study, we used process mining to compare the course engagement patterns of these groups. We found that throughout the course, the intrinsic group was the most engaged, but the prosocial group became the most engaged by its end and was more engaged in the course's forum. Our findings enhance the understanding of the relationship between motivation and engagement and suggest that MOOC developers may want to consider why some groups are less engaged and change the course structure accordingly.