Your point is well taken, but in the US, at least, a limited liability company is also an entity that you can form like a corporation, or a partnership, so the words don't necessarily conform to their dictionary definitions and are, perhaps, more interchangeable than you suggest.

I also think there's a broad divide in the world between those who think that corporations are dehumanizing and those who think of them as simply a group of people, like the dictionary definition of a company.