In algebra geometry terms the difference between superellipsoid and superellipse

is that superellipsoid is a closed surface, of which the sphere and ellipsoid are special cases, whose parametric equation is x = a.cos^2/rt, y = b.cos^2/rt, z = c.cos^2/rt while superellipse is a geometric shape constituting a transition between a rectangle and a circle; a closed curve, of which the circle and ellipse are special cases, whose parametric equation is x = a.cos^2/rt, y = b.cos^2/rt.