You're making a common mistake and confusing corporatism with corporatocracy.

The 'corporations' of 'corporatism' are not the financial, profit-driven corporations that we think of when we hear 'corporation' today, but theoretical collective organisations of the different groups of society - usually at a minimum business owners, labourers and employers, but often possibly including intellectuals, farmers, bureaucrats, or almost any other group that you could name. The idea is that policy should be made by negotiations between these corporate organisations.

It's a philosophy that used to be quite popular in the early 20th century, especially among Catholic politicians (such as the Centre Party) but also among some fascist thinkers, although few fascist regimes were actively corporatist (Fascist Italy did set up corporate bodies but they were mostly talk shops so it was not actively corporatist). This may be because it was mostly a reactive philosophy used by moderate conservatives and liberals (in the European sense) to try to address some Marxist and Socialist critiques of the capitalist state without actively conceding control to Labour.

So the key to understanding corporatism is to realise that the word "corporation", at least in its most literal meaning, can refer to any group of people working together towards a common purpose. What we think of as a 'corporation' in the modern day is just one type of corporation.

When you talk about 'corporatocracy' you are presumably talking about a policy that prioritises the wellbeing and profit of financial corporations. The Centre Party, while not actively anti-finance, wasn't thinking of this when they called themselves corporatists. Corporatocracy is a less politically dense concept than corporatism, not least because the term is usually only used as an accusation - almost nobody self-describes as a Corporatocrat. It's further confused because a lot of people use the term 'Corporatist' to describe Corporatocratist policies or systems.

Source: Corporatism and Comparative Politics, ME Sharpe.