Corporatism is the idea that society and the economy of an area or country should be organized into major interest and/or industrial group (i.e corporations) and the representatives of whichever interest group (corporation) would settle any problems through negotiation and joint agreement. Under corporatism the labor force and the management of whichever industry belong to an industrial organization aka corporation. The representatives of each corporation would settle any disputes (like wage disputes) through negotiations with the collective body of the corporation. That's the basic idea behind corporatism or corporatist states as I understand it. Usually it functioned according to the will of some dictator, like Mussolini, Franco, Hitler...etc, rather than the representatives per se. It's mostly associated with Fascism, but not all corporatist areas/countries are/were fascist dictatorships. Some modern examples of countries that could be considered corporatist states would be like China, Iran, Russia and a few others.
Corporatism could be summed up as being de facto nationalization. Like private property (means of production) isn't exactly nationalized per se, but the way it's controlled via tight government intervention/regulations makes it seem like it has been nationalized. The ideas of corporatism partly originates with some dude named Adam Müller. Mussolini was the first who put the coporatism into practice, I believe.
Also, corporatism doesn't have much, if anything, to do with those big business corporations like in the US today. Some think it does for some reason. I suppose that is because the word "corporation" is used. Those big business corporations that we know of today in like the US are examples of capitalism. Anyhoot, that's my understanding of corporatism.
Capitalism is an economic system based upon individual "rights" and private property "rights" (means of production) where all goods (capital) produced are owned privately by the owner of the means of production, rather than the ones that produced said goods, like the worker. There is a degree of government intervention in capitalism.