There isn't any. The circumference is just a special name for a perimeter of a round shape.
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The length of the perimeter is the circumference. The perimeter itself is the boundary between the interior and exterior of the circle. The perimeter of a circle is called the circumference
The perimeter or circumference is the distance around a circle whereas the diameter is the distance across a circle through its centre.
Circumference is only used for circles. Perimeter is for every other 2D shape.
The perimeter of a circle is its circumference
When the shape is a circle, then the perimeter is called"circumference".The circumference IS the perimeter of a circle.