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.