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Plane assumes a flat surface, where the angles of a triangle always add up to exactly 180 degrees. Spherical assumes a curved surface (such as the surface of the Earth, where the angles of a triangle add up to more than 180.

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There are many differences but perhaps the main difference is to do with the parallel postulate - or equivalently - the sum of the interior angles of a triangle. The sum of the interior angles of a triangle that is drawn on a spherical surface can be much greater than 180 degrees. One consequence is that given any line and a point that is not on that line it is possible to draw more than one lines through the point which will not meet the line.

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10y ago
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Q: What is deference between plane trigonometry and spherical trigonometry?
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