The main difference between Perimeter and Circumference is that the Perimeter is a path that surrounds an area and Circumference is a linear distance around the outside of a closed curve or circular object. 6park.com
Perimeter
A perimeter is a path that surrounds a two-dimensional shape. 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 circle or ellipse is called its circumference.
Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter.


Circumference
In geometry, the circumference (from Latin circumferentia, meaning "carrying around") of a circle is the (linear) distance around it. That is, the circumference would be the length of the circle if it were opened up and straightened out to a line segment. Since a circle is the edge (boundary) of a disk, circumference is a special case of perimeter. The perimeter is the length around any closed figure and is the term used for most figures excepting the circle and some circular-like figures such as ellipses.
Informally, "circumference" may also refer to the edge itself rather than to the length of the edge.