Knot documentation is here: http://docs.mcneel.com.s3.amazonaws.com/rhino/6/help/en-us/popup_moreinformation/knot.htm
This documentation is incomprehensible because it is devoid of drawings. I made simple drawing, shown below, which may be used to define knot. I drew the red curve first. Then I drew the green line between the control points. Finally, I drew the blue line. The blue line is perpendicular to the red curve and the green line. The knot is part of the red curve. It is defined as the intersection of the red curve with the blue line.
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Kink documentation is here: http://docs.mcneel.com.s3.amazonaws.com/rhino/6/help/en-us/popup_moreinformation/kink.htm
It does not explain how the kinks are related to control points and knots. To the best of my knowledge, the kink is a place where at least two control points are in the same place.
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ChangeDegree command has Deformable option. Its name suggests that if you set it to No, the curve will not be deformable. In reality this option has nothing to do with deformability. Documentation mentions ‘knots of multiplicity’, but does not explain how these ‘knots of multiplicity’ change behavior of the curve.