The notion that product development (engineering a product) is the same a Managing the efforts of the project that produces that product is a popular myth in the agile community. This notion was being taught to graduate students at one time. When I was asked to contribute to a course on "Managing Software Projects," I was joined by a product development manager from the worlds most popular electronic payment processes business. We approached the issue from the point of view of Scrum and general project management.
The glue that connected these threads together is CMMI DEV V1.2. For many reasons this is a good starting point for the discussion of software development processes and the structure of software development projects. As well the University hosting the graduate programs is also the university hosting the Software Engineering Institute.
Here's a slide taken from a course on this topic and the picture that connects the dots between product development and managing projects performing product development
If you can accept that methods like Scrum are applied to the development of products, then the connections between Project Management and Product development can be made. Note there are two other Process Groups in the business of software products, Support of the processes and Process Management.
Doing is not the same and Managing the Doing
Now certainly "doing" has elements of management. We're not robots. And doing and the management of doing have overlapping processes. But the management of doing has exclusive elements as well.
There may be a case - I'm waiting for the details - where the processes of Scrum can be applied to the general management of a software development project.
