Parabole is a alternative form of parabola.

Parabole is a descendant of parabola.

In rhetoric terms the difference between parabola and parabole

is that parabola is the explicit drawing of a parallel between two essentially dissimilar things, especially with a moral or didactic purpose. A parable while parabole is similitude; comparison.

As nouns the difference between parabola and parabole

is that parabola is the conic section formed by the intersection of a cone with a plane parallel to a tangent plane to the cone; the locus of points equidistant from a fixed point (the focus) and line (the directrix) while parabole is similitude; comparison.