Also, the wide lenses on most phones are actually very heavily distorted nearly to the point of being fisheye, and made rectilinear with processing.
Not just phones. Most wide-angles for "serious cameras" have distortion and rely on digital correction. See [0] for an extreme example in the form of a 16mm Canon, which is much less wide than the iPhone lens.
[0] https://photographylife.com/reviews/canon-rf-16mm-f-2-8/2
For fisheye, I guess it would have been more accurate to say: the perspective distortion is present in both photos and is stronger for the iphone photo due to a shorter effective focal length, and there is no noticeable fisheye/barrel distortion in the iphone photo.