How can an "S Corporation" be either a corporation or a limited liability company?

This is an historical artifact of the tax code. Subchapter S was adopted in 1958, long before limited liability companies came into existence. It was intended to allow small business corporations to have the benefit of "pass through" taxation while retaining the benefit of limited liability by operating as a corporation. In 1958, an "S Corporation" could only be a corporation. That changed with the advent of limited liability companies in the 1990s, but the terminology has remained the same.