Corporatism vs. Capitalism

Leave aside for a moment different definitions and interpretations of the term broadly. What those who self-identify as capitalists mean by the term capitalism is essentially a liberal free-market.

Understanding the term that way, the difference between capitalism and corporatism is ultimately consent. What is or isn't voluntary and peaceful.

Under capitalism, if I have a widget and you have a dollar, and I want the dollar more than the widget and you want the widget more than the dollar, we can consent to a voluntary trade for mutual benefit, where we're both better off and by extension society is. There is no fixed pie, no automatic losers when someone else wins, and people benefit themselves through providing benefit to others (even if the rate of growth is unequal). The incentive structure is such that even selfish bad people are utilized for the public good and overall progress is made through incalculable amounts of peaceful interactions among private individuals benefiting the whole through trying to better themselves.

Under corporatism, the state can steal through taxation and use the proceeds to subsidize large corporations, or let them through regulatory capture write laws to benefit themselves or disadvantage their competitors. This is a fixed pie and a zero sum game, and instead of consent, it relies on force, violence, or the threat of violence inherent in using the state to achieve its ends. The incentive structure is to get big enough that nobody can compete with you without risking you using the government as muscle. One's gain is inherently someone else's loss, because not all interested parties need agree.

These two terms... capitalism and corporatism... It's not merely that they're not complimentary. They're inherently incompatible. The only connecting tissue is that there is a danger of capitalism becoming corporatism when economics of scale are large and antitrust lax.

There's other definitions of capitalism one could use. The term was coined by Marx and he had a different vision in mind. But if your self described capitalist friend says "what you're complaining about is corporatism, not capitalism", this is what they mean. If it makes you feel better to pedantically point out that they're describing free markets or something and that there's differences in terminology between capitalism and free markets, fine... but the overall point remains.