Product management is a relatively new role specially in technology companies. The evolution of the role came from the Product Marketing Manager role common in many companies way before the new role but it goes far beyond the marketing part.
It is important to note that Product Managers don't all have the same role and responsibilities in all companies, even though the name of the role might be similar.
The differentiating factors I've seen include:
1. True owner of the product vs. the influencer.
This differentiation is typically dependent on the size of the comapny, where in smaller companies a PM can actually own the product including the build, launch and ongoing improvement. And in larger companies the PM is more of an influencer and does not actually own the product. There is definitely semantics involved in the definition and description but in general this has been my experience.
2. Engineering Led or Product Led organization.
Most traditional tech companies have the engineering team as the builder and owner of the product, and product's involvement and role is a matrix role. Some companies have engineering report to Product which creates a more clear and executable responsibility path.