What is the difference between square centimeters and centimeters square?

"Square centimeters" is a measurement of area. "Centimeters square" describes a square shape X centimeters on each side. "4 square centimeters" would be an area 2 cm wide by 2 cm long (or an equal area in any shape. "4 centimeters square" defines a shape having four 90 degree angles and 4 sides of 4 cm each, which has an area of 16 square centimeters.