A superellipse is only a squircle if a and b are 1. As with squares and rectangles, all squircles are superellipses but not all superellipses are squircles.
If a and b are equal* (not just 1). A circle is a special case of ellipse where a and b are equal and the eccentricity is 0. This is the same principle.
Since Archimedes until and including Euler, paraboloids and hyperboloids of 2 sheets were named "conoids" (parabolic conoids and hyperbolic conoids), which makes more sense than "hyperboloid", because they look like rounded cones (Archimedes analyzed only their variants that are surfaces of revolution).
The hyperboloid of 1 sheet has been named by its discoverer (Christopher Wren) as "hyperbolical cylindroid", which is also more suggestive of the shape of this surface.
The change in terminology to paraboloids and hyperboloids was justified by the fact that in the older literature "conoids" and "cylindroids" had been used only for surfaces of revolution, because those with elliptical sections were not discussed before Euler, but this justification fails, because we now also talk about elliptical cylinders and cones, so there the names "cylinder" and "cone" have been retained, even if they also referred strictly to surfaces of revolution in the older literature.
A more consistent terminology would have been to retain the names "spheroid", "cylindroid" and "conoid" that were used in the old literature and add "elliptical" whenever they are not surfaces of revolution, like it has been done for "cylinder" and "cone".
I think the novelty of the article was in the 2nd image, and why it's so much less well known. But my theory is there are not as many applications for symmetrical curvy lines that diverge than symmetrical curvy lines that converge.
