It seems that you did your design in quadratic curves and, for some odd reason, the conversion to cubic failed spectacularly.

Are you copy-pasting the design? From where?

The font was originally designed in Fontstruct.
I had someone work on the kerning, and they said it must have happened early on when they converted it from .TTF to .OTF!
But it sounded very odd to me, as I didn't know whether that was possible.
Does that sound true to you?
It's very odd that the angled one has added in more points!

My first thought is that they used something other than FontLab Studio to do the conversion from TTF to OTF. I’ve never seen that result before in a conversion.

FWIW, in the image you show, the angled one and the curved one have the exact same number of points. It's just some of what used to be off-curve points defining the shape of a curve, are now part of a straight line segment.