What's the difference between perimeter and circumference when they mean the total length of the boundary of a two-dimensional geometric shape?
Circumference is a special case of perimeter. Both describe the total length of the boundary of a two dimensional figure, but circumference specifically refers to the perimeter of a curved figure or arc. Therefore it only applies to circles, ovals, ellipses, arcs, etc.
In ordinary usage, perimeter almost always refers to the boundary itself, while circumference is more likely to refer to the length of the boundary: you might hear someone ask "what's the circumference of the circle?" (expecting an answer like "10 cm") but you'd never hear them ask "what's the perimeter of the circle?" for the same answer.
1The real reason why you'd never hear that could be as @phonixheart6 stated in his answer.– KrisOct 21, 2012 at 4:02
Circumference is the linear distance around the outside of a closed curve or circular object. The circumference of a circle is of special importance to geometric and trigonometric concepts. However circumference may also describe the outside of elliptical closed curves. Circumference is a special example of perimeter.
A perimeter is a path that surrounds an area. The word comes from the Greek peri (around) and meter (measure). The term may be used either for the path or its length - it can be thought of as the length of the outline of a shape. The perimeter of a circular area is called its circumference.
However, I'd be constrained to say this is general reference question.