A Product Owner is any stakeholder who has an in depth understanding of the stakeholders requirements and who has the ability to communicate those requirements to other members of the scrum team.
While a Product Manager is anyone who leads a product development project.
A Product Manager needs to understand the customers’ needs as well as find ways to fulfill those needs.
This sounds very similar to what a Product Owner does except that the Product Owner does this in an agile setting.
Product managers are involved in every stage of the product management process from business case creation, requirements elicitation, requirements documentation, product design, product testing and product delivery.
A Product Manager can become a Product Owner if they are part of an agile team i.e Kanban, Scrum or a Scrumban Team, if they apply the agile methodology and uphold the agile values.
While a Product Owner can become a Product Manager if they expand their product development role outside the scope of the agile methodology.
So basically a product owner is an agile product manager.
A real Product Owner should not only be limited to IT product development.
They should be involved in product development in all areas of the organization such as sales, marketing and operations but in reality, you only find product owners in IT product developments while product managers can be found in other departments in the organization.
This is because agile methodologies are mostly used in IT projects.