An arc length is is the distance 'walked' along the edge of a circle. An arc measurement is a number (measured in degrees) representing the amount of rotation.
Arc length is a portion of the total distance traveled along the edge, which is the circumference in the case of a circle. Arc measure is a portion of 360 degrees (1 full rotation).
The ratio of arc length : circumference is equal to the ratio of arc measure : 360 deg, so any of the three variables (arc length, circumference, or arc measure) can be determined through a proportion involving the other 2.