Answer: the same. It's just that our default frame of reference is the surface of the Earth. Relative to that frame of reference, the sun is in fact moving
We were talking about the reliability of intuition versus sense perception.
I'm not sure, though, that the intuitive appearance of the sun moving is the same sense of intuition as some philosophers use. We don't perceive the Earth to be in motion, and from a frame of reference based on the surface of the Earth, the sun actually is in motion. The mistake was thinking that this was an absolute reference frame. I would say that was more a misinterpretation of our perceptions than an intuition. People could give reasons for why they thought the Earth was motionless: wouldn't buildings fall down, and birds find it harder to fly in one direction rather than another? etc. It wasn't just an intuition in the sense that it's something that people believed without being able to say why. They could say why they believed it, and they could relate it to perceptions to justify those beliefs. I think there's a distinction there.
That's ok, I don't think it's a good argument. It's based on redefining the word "intuition" to mean something else, e.g. "5+7=12" is an intuition according to the article's definition.