But public services and government owned are also corporations. Corporation doesn't mean 'for-profit public company'. It just means a group with a legal identity.
For example in my country corporations are strictly for profit. It is also not just a "corporation", but a "business corporation" (there is no "corporation" by itself). Public companies are either publicly traded private companies and the state holds stock, or "publicly-owned enterprise" or another special category.
The point was that I think there is value in distinguishing public companies and private companies because it's completely different from employee's and career viewpoint.
For example British Broadcasting Corporation.