The style options in Knot Display affect the entire graph, and they affect how the graph is displayed but its shape is not altered. These features are those that can be changed on an exported SVG without changing the path control points.
Depending on the design there may be multiple ropes that make the knot, specifying multiple colors will cycle the defined colors when drawing each rope. If only a single color is defined, the entire knot will have that color. Knotter also supports automatic coloring that assigns a distinct color to each rope in the knot, this may be useful to study the topology of that knot.
The width is the thickness of the rope tied in the knot.
If the knot style results in some sharp angles, this affects how they are displayed.
The options in Knot Style instead affect the shape itself. Their exact meaning depends on the edge type and cusp shape. Every feature in Knot Style can be configured on a per-node basis via the Selection Style dialog.
Size of the curve control handles, its behaviour depends on the edge type. In general, it controls the way a ropes approaches the center of an edge and the cusp point.
Distance between the ends of a loop then a rope passes under another rope. It may change meaning for different edge types.
Minimum angle between edges for which a cusp shall be drawn.
Distance of the cusp point from the node position.
The style used to draw a cusp.