From the front end of the software interface to the point in which the stepper or servo motor controller inputs are generated from algorithms based on the sections of geometry data plugged into it. That takes on forms of translation software to configure the variables into a format the device or module can react to.
Much of this will be OEM chip oriented. Each may have its own process to do the same function.
In an attempt to keep it generic rather than proprietary. Here is a link that lays out some of the basics in motion control. It describes several approaches in the configuration options available.
Trying to create the entire system on your own takes quite an array of knowledge. Taking advantage of the ready made black box's on the market makes it so much easier to just generate the path via software and let the controller do the hard part. A lot less time involved when the majority of the motion engineering has been done for you at such a cheap price. That comes from my preference in working 100 hrs on something I know verses 1000 hrs on something I don't and not coming close to the desired results.
Motion Controllers 101