Complex sentence: Without further qualification, the crossing number allows drawings in which the edges may be represented by arbitrary curves; the rectilinear crossing number requires all edges to be straight line segments, and may differ from the crossing number.
Split into simpler sentences: Without further qualification, the crossing number allows drawings in which the edges may be represented by arbitrary curves. A variation of this concept, the rectilinear crossing number, requires all edges to be straight line segments, and may differ from the crossing number.