My 10-22mm lens does not distort things in the way that photo shows. Nor does my 16-35L.

There are super-wide angle rectilinear lenses (non-fisheye) as well as super-wide angle fisheye lenses. My understanding is that fisheye lenses make no attempt to correct for the obvious warping and distortion; whereas rectilinear lenses include a number of secondary lens elements specifically to try and correct such.

A good super-wide rectilinear, when held horizontally, will generally show a familiar view of the world. A fisheye lens of the same focal length will always show a curvy view.