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.
Among all squircles having arbitrary exponents (|x|^p + |y|^p = 1), PI (3.14159...) is the smallest value of ratio of circumference to diameter.
There is a paper on this with the pithy title "π is the Minimum Value for Pi": https://www.tandfonline.com/doi/abs/10.1080/07468342.2000.11...
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.