Motion that repeats itself after a regular interval of time is called a periodic motion, whereas a motion in which an object covers an equal distance in regular subsequent intervals of time is called a uniform motion.
As in periodic motion, the motion is repeated in regular intervals of time, therefore the object covers equal distance in those regular intervals of time. Because of this, we can say that the object is also demonstrating uniform motion.
Although not all uniform motions are periodic as they may or may not repeatedly trace the same path.