Can a circumference of a circle be the same as the area of the circle?

No, because the circumference is a linear measure whereas the area is a square measure. However, they can have the same numerical value.

If a circle has radius r cm, its circumference is 2*pi*r cm while its area is pi*r2 cm2. These two are numerically equal if 2*pi*r = pi*r2 that is, r = 2 when both measures are 4*pi = 12.6 approx.

The fact that the dimensions are different means that, in other units (inches for example) the same circle will not have equal circumference and area. In this case, the circle has a circumference of 4.9 inches and an area of 1.9 sq inches: not the same.