What is also an example of stunning ignorance here is that a corporation (and by extension capitalism) cannot exist without the laws and the coercive power of the government to enforce them. One can argue a government is whoever can enforce rules for markets to function.
This, I think is the heart of the lie that people miss. Which leads to myths being established that companies/markets are something different from governments and not an extension.
There is a whole body of thought about corporations existing outside of governments, anarcho-capitalism. In fact, the way I equated corporations and government relies on assumptions from this view.
You're coming around to the equating from a different angle, but it feels a bit lacking to me because corporations certainly can exert pressure on governments and asserting that corporations are reliant on governments would seem to downplay this dynamic.
Corporations that competed with governments had armies historically, trade corporations like Hansa or East Indies operated that way. So as long as they aren't fielding armies they are not competing with governments, just influencing them a bit.
In the large as to their goals, effects, and competition with each other, sure. I was talking about individual freedom, and in that context they are both capable of applying coercion to individuals.
This, I think is the heart of the lie that people miss. Which leads to myths being established that companies/markets are something different from governments and not an extension.