Yes, before MBAs took over, project management was more related to actually what happens in the project, GANT charts, stuff like Microsoft Project, resourcing team, setting the overall plan what goes where, who's available, when are vacations allowed,...

Product management was interfacing with the client, understanding what is actually supposed to be built as vision, understanding UI/UX before that became a field of its own, coordinating usability sessions, and so forth.

Naturally they have common touch points like what is possible from the vision, given the actual budget and available resources, expectation management and what not.

Product Management = Big picture product vision. Features and Priorities. Market trends/strategy, Voice of customer

Project Management = Day to day to execution, logistics, resources, schedules. Scheduling meetings, sending out meeting minutes etc

Program Management = Team management towards delivering business goals/product launches on schedule

Where its tricky is the differentiation between project and program management. IMO we dont really need both terms or both roles, causes uneccessary/unnatural separation of responsibilities

What actually happens in most (small) businesses is one person gets lumped with all these jobs and the business is regularly surprised they're constantly over-worked and under-delivering

I often see product and project management combined. Usually it results in mediocre execution on all fronts. The last PM I worked with didn't even understand the product.

I've written a reference because I've had this conversation so many times, haha

https://jzelinskie.com/posts/p-what/

There's even more. In games, we also use the term 'Producer' which manages the production, ie they're mostly a project manager. The design team is the product design role. Even here, the producers can and will dabble in design discussions in so far as is needed to meet timelines.

The nice thing is no one gets inflated with a manager title they think makes them the boss of every department. You get engineering lead, production lead etc.

Product management is what you want to do, project management is what you actually do, program management is what you say you do.