Main Difference
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.

Perimeter
A perimeter is a path that surrounds a twodimensional shape. The term may be used either for the path or its lengthâ€”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 circularlike figures such as ellipses.
Informally, “circumference” may also refer to the edge itself rather than to the length of the edge.

Perimeter (noun)
The sum of the distance of all the lengths of the sides of an object.

Perimeter (noun)
The length of such a boundary.

Perimeter (noun)
The outer limits of an area. circumference

Perimeter (noun)
A fortified strip or boundary usually protecting a military position.

Perimeter (noun)
An instrument for determining the extent and shape of the field of vision.

Circumference (noun)
The line that bounds a circle or other twodimensional figure

Circumference (noun)
The length of such a line

Circumference (noun)
The surface of a round or spherical object

Circumference (noun)
The length of the longest cycle of a graph

Circumference (verb)
To include in a circular space; to bound.

Perimeter (noun)
the continuous line forming the boundary of a closed geometrical figure
“the perimeter of a rectangle”

Perimeter (noun)
the outermost parts or boundary of an area or object
“a perimeter fence”
“the perimeter of the garden”

Perimeter (noun)
an area away from the basket, beyond the reach of the defensive team
“he was very patient in working the ball around the perimeter”

Perimeter (noun)
an instrument for measuring the extent and characteristics of a person’s field of vision.

Circumference (noun)
the enclosing boundary of a curved geometric figure, especially a circle.

Circumference (noun)
the distance around something
“babies who have small head circumferences”
“a rope two inches in circumference”