why is it impossible to create an arc with the freeform tool?

I create a 90 degree arc, radius = 3 units, then I create a freeform curve with exactly the same control points, and I get 2 different curves. even moving the points of the arc, then placing them back to the original spot, generates a perfect quarter circle, but it is impossible to mimick that with only 3 points of a freeform curve. see below, the selected one is the freeform curve. both curves have show points on.

it seems that there is different formula behind the 2 types of curve, but when integrating the arc in a larger path, and disassembling it again, the properties stay the same.

it's not a big deal, but it puzzles me...