Which they acknowledged

They are more than "slightly" different. A product manger is a creative professional. A project manager is an administrative professional.

Creative writing, maybe? Outside of founder-level product managers, of which I have worked with several who are actually creative, I remain unconvinced there is much real difference.

Product Managers - identify problems to be solved, decide/play a role into what features goes into MVP or a release, talks to customers, comes up with/designs the solutions (functional solutions) to the problems (aka features and how they interconnect), do UI designs (major UI designs can go to the UX team, smaller UI designs stay with product manager), etc

If your company is using the sprint model, the Product manager is not doing much of project management.

At the end of the day, what a PM does depends on the company and how they use PMs

So you say. However, I've been at companies where PMs are running the daily sprint / scrum meetings.

As a product manager (technically "program manager" at Microsoft, but it's roughly the same as product managers across the industry), project management is one of the many things I do, in addition to the list above. But I am explicitly not a project manager in that I'm supposed to minimize time spent on that and share some responsibilities in that space with my engineering counterparts.

I don't think I've ever worked someplace where the product manager role is fundamentally creative. It's their job to j understand stakeholder concerns and coordinate the team around solutions. But designers are typically doing the creative UX work.

Not really. When I had a "product manager" title, I had to do plenty of "project management".

I've found there's some status thing with 'product manager' (particularly at Google) and product managers will make sure you know the difference.

In practice I'm not sure how different they actually are. Typically when someone is desperate to say how much better/harder their title difference is it's because it's not really obvious otherwise.

At my workplace, the product managers are part of the marketing department, and interface with the sales force. Most of them have MBA's.

The project managers are in the engineering department and interface with the engineers, suppliers, operations, etc. Most have engineering degrees.

They work out most of the project documentation together, such as the specifications, budget, schedule, etc.

It’s almost as if the roles are a little bit different at each different company! I’ve worked places with a single person doing these roles, and places where they were separate people. Also worked places without someone doing them, and that situation is consistently awful.