Lathe control and rotary are different in my knowledge.
I think lathe needs radius based spindle speed control and rotary needs constant surface speed control which are totally different things as far as I understand.
How I think they are different is that with lathe the radius based spindle speed control is what is needed and how that works is that the spindle speed is automatically adjusted based on how far an axis is from the 0 coordinate. E.g. the Z axis distance from 0 sets a proportional spindle speed.
And the rotary to work optimally requires constant surface speed control where the feedrate needs to be compensated (again based on the radius or the Z distance from 0), just like if e.g. the A axis was an Y axis, I mean like if it was a XA plane instead of a XY where the A axis is rotating and the feedrate compensation changes as the Z axis moves closer and further the 0 coordinate.
Please correct me if I'm wrong.