The data often "knows" where it will be displayed, and is designed with that knowledge. To go to the absurd extreme here, the data is just 1s and 0s, not pixels

The data often "knows" where it will be displayed, and is designed with that knowledge. To go to the absurd extreme here, the data is just 1s and 0s, not pixels or samples or anything more. Of course that's nonsense, because the data has context and the arrangement of those samples or pixels has a purpose. Sometimes that purpose is to serve as a sampling of a real-world continuous image, other times it is to describe the arrangement and color of tiny little squares on an LCD screen. Depending on what context you're working in pixels can be squares, or may not be.