Corporatism actually refers to the government, businesses, unions, church, and other institutions (the exact institutions included varying between forms of corporatism) working together as parts of a body; it is not derived from the use of “corporation” for a business entity.
It's corporatist, but not socialist (you can probably make an argument that non-libertarian socialism is also corporatist, but not vice versa.)
But, yeah, the cult of manichean capitalism tends to use “socialism” as the generic label for “opposed to capitalism”.