I find that there's a tremendous amount of prejudice against certain words in the Scrum community and "manager" is near the top. A business can and will give their roles any title they feel is appropriate. I would bet the farm that in some companies, the Scrum Master role is more aligned to a Project Manager of old and that Agile Project Manager role is more aligned to the Scrum Guide’s definition of the Scrum Master. So far no help, right?
Most businesses that are or will be transitioning to Scrum will have an Agile champion on board to guide the transition. I was this person at my previous company and after some time the role of Scrum Master was identified and added to HR’s list. However, before that happened, the person in the Scrum Team coaching and helping the developers and product owner was known as “Scrum Master”. This happened due to training and coaching the software and product management departments received during the transition to Scrum. The internal view was that the servant-leader of a development team was called “Scrum Master”. The external view of the role as projected by the HR department, possibly following 10 – 20 years of tradition, might have still have the role listed as “Project Manager” but now with the added term “Agile” plopped in front. This shouldn’t be too much of a surprise as the adoption of Scrum starts within the software department and will only spread once the successes due to the application of Scrum are recognised. As the Agile champion, my focus was on the software department and not HR, (in the beginning). After a couple months and Scrum had an obvious foothold in the company, efforts to re-align HR roles and role descriptions (Scrum Master, Development Team Member, Product Owner) began.
As a practicing Scrum Master and I saw a job ad that said, “Agile Project Manager”, I would apply with the knowledge that the role is most likely that of a Scrum Master for a company in transition (or possibly stuck in transition). I might find out otherwise at the interview but that’s the point of the interview: the prospective employer and prospective employee determine if there exists a common understanding of expectations and responsibilities surrounding the role. Some may see this as waste but as the interviewee, I see interviews as a learning experience even when the ultimate outcome is no job.
One of the responsibilities of the Scrum Master in the Scrum Guide is, “Leading and coaching the organization in its Scrum adoption”. This is where it can be argued that the Scrum Master is charged with aligning the roles and role descriptions in HR with the roles and descriptions found in the Scrum Guide. If the Scrum Master(s) are unsuccessful in doing this today, then it means they try again tomorrow, and the next, and so on. As long as the internal application of Scrum roles is correctly aligned with the Scrum Guide, then this view external of the Scrum Team might be an annoyance but not necessarily a terminal problem.
In the final analysis the Agile coach and Scrum Masters need to pick their battles with an eye on impact and results. Getting management and the Scrum Team following the Scrum framework is to me, job one. Pulling the rest of the corporate structure in line with Scrum role descriptions i.e., HR and management, is of secondary concern in my view.