In a Scrum team, the Product Owner (PO) turns users' needs into a prioritized list, communicates with stakeholders, and translates customer pains into user stories.
The Product Manager (PM) sets the long-term direction, coordinates with the rest of the company, and seeks growth opportunities.
The Scrum Master facilitates Scrum events, removes roadblocks, and promotes Agile values like continuous improvement and collaboration.
Blurring the lines between roles can lead to missed priorities, lack of coaching, and a deterioration of the Agile process.