Project Manager is a manager, it's a role from a formal process (waterfall). Product Owner is not a manager, it's an agile role.
You can't compare them directly.
P.S. In real life PM/PO are almost the same -- as people usually don't care about following metodology. PM/PO is just a kind of team's boss.
P.S. In real life PM/PO are almost the same -- as people usually don't care about following metodology. PM/PO is just a kind of team's boss.