The narrow definition of corporatism is basically just the public-private interweaving of government. Communism is just as much corporatist as fascism -- the main difference being that in communism the trade bodies are considered part of the government rather than part of the industry.

Fascism is more specific because it also encompasses fostering/breeding tribalistic tendencies (bigotry, nationalism, i.e. "othering") in society at large. In contrast, corporatism doesn't prescribe how the rest of society interacts.