As soon as an article states you can use “product manager” and “project manager” interchangeably, you can immediately assume the author has no idea what they’re talking about. Convenient this article did that early on, saves everyone a lot of time.
A PM's job is to be the owner of the "problem space", while the engineering teams job is to be the owners of the "solution space".
Fords point was that his customers would only ever tell him about solutions they wanted (faster horse). When in actual fact what mattered to Ford was the problem (current modes of personal transport being expensive, unreliable, uncomfortable, slow, single-person).
Any good PM should be able to explain this to you. OP has never worked with a proper PM apparently... Just BA's and Project Managers that wanted a pay bump.
This is quite common. Lots of ex-project managers are now called product managers or scrum masters. But they're actually project managers.
For example, I tend to be the guy on the panel all the other PM's hate because I taught myself to code so that I could have deeper empathy for how my engineering teams work and now I advocate for all PM's needing to be at least moderately technical.
Rocking the boat certainly doesn't make you popular haha
Also, Product has in some places gone from a valued member of the team to a ruling class, with all the faux problems that generates.
It's a funny one!
The actual boundaries tend to be a bit fuzzy because a lot "product management" comes down to doing whatever the team needs in order to make sure a good product is delivered, and by necessity product managers often do a substantial amount of project managing.
Typically you'll see people conflating "program management" and "product management" in tech. You don't usually see "project management" in that mix since that tends to refer to a more industry agnostic discipline.
The key responsibility (and purpose) of a product manager is to provide a coherent vision of what the product needs to be successful and define what the ongoing projects' goals should be to effectively improve that product.
Engineer - how to build; project manager - how to organize building; product manager - what to build.