There are several differences between product owner and product manager. The answer you get will vary depending on if you talk to someone with a product management background versus someone who has spent most of their time as an agile coach or scrum master.
The following discussion is based on what I’ve seen most often in practice:
Product manager is generally a job title that exists regardless of the approach that an organization takes for product development. Product owner is generally a role created as part of the Scrum framework for product development (in practice mostly used for software development).
A product manager is concerned about all aspects of product development, both facing externally to understand customer’s problems and market needs and the internal aspects of developing a solution. Product owners tend to be primary concerned with internal issues and primarily interact with the rest of the team developing the product.