Are you arguing that there is no difference between UI designers and graphic designers? It may all seems like "silly design stuff" but I promise you -- there's a big difference between the two. For example, UI designers usually need to be able to code (if perhaps only rudimentarily).

Or perhaps you're implying that there is no difference between UI designers and product designers? Admittedly, sometimes those are the same person, but usually the person who fills the PD roll is a manager or CEO (if at a startup). They'll certainly consult with the UI designer (and eng), and they may design most of the product with the UI designer. Or they may not. Not necessarily the same job. It really depends on the people and the company.

If this seems like bullshit to you then...I'm sorry? That's how most of the industry works (at Google, at Apple, at ...). There are not these strange creatures called "designers" who do everything and have all skills (some do exist! but they are shockingly, painfully rare. And they're usually not in charge, so it's hard for them to do product design).

Maybe you meant something more specific, but you seem to be implicating yourself. Here's what you said above:

"If a UX designer produces mocks and designs, they're a designer. If they produce software prototypes, that's called an engineer."