I think project management differs in different industries is in terms of regulations involved on a project. For instance, projects in the biomedical industries need to take into consideration the FDA regulations, such as 510(K) clearance. While construction site has to fulfill safety and health regulation established by Occupational Safety and Health Administration (OSHA).
If I were to be a great PM for medical devices project, it does not necessitate that I would be a great PM in a software company. Yes, there is one book that covers the fundamental elements required for project management. However, a PM needs technical knowledge in the field he or she is working in to ensure how the project will unfold. A great PM in medical devices project most likely has some technical knowledge in the projects he or she is managing. However, if that PM is thrown into a software company to work on a program like Microsoft Office, the PM would not have the necessary technical knowledge on how to proceed on with the project. Furthermore, some technical knowledge is important because it gives a PM better judgment on how to handle the project especially for the risk management aspect of project management and make a decision on costs. Moreover, compared to a software company and medical device company, the regulations for a project to meet and the requirements documents for a specific project would greatly differ. For instance, for the software company, the government requires cybersecurity regulation, such as the Data Security and Breach Notification Act, which requires software companies to provide notification if an individual’s security is breached. A phenomenally PM in a medical device company may not be aware of this regulation because this type of regulation is not common in the biomedical industry since most federal regulation on devices is regulated by the FDA.

References
https://www.linkedin.com/pulse/20141005232306-13261887-project-management-across-industries
https://www.congress.gov/bill/114th-congress/senate-bill/177