But this is a bit silly surely? If they are different ways of talking about the same thing then one might as well label oneself a 'mentalist' and say "physical processes don't 'have mental effects', they just flat out are mental processes."
I think what you're going for is a species of monism maybe? The idea that Thought and Extension are attributes of one Substance?
We’re talking specifically about mental processes.
I think we agree that all weather is a physical process, but not all physical processes are weather. Similarly all mental processes are physical, but not all physical processes are mental.
Nevertheless it’s not that the physical atmospheric processes create weather as aside effect or product, they are the weather. Similarly mental processes are a class of physical processes.
Idealists take the opposite view. They think there are only mental processes and the physical is a class of, or product of mental processes.
I think what you're going for is a species of monism maybe? The idea that Thought and Extension are attributes of one Substance?
https://plato.stanford.edu/entries/spinoza-attributes/