Why do moving back and forth, and moving in a circle look the same on a graph of position versus time?

Because in both kind of motions, the position is periodically repeated. Both are simple harmonic motions.

Explanation:

Moving back and forth means that the moving object goes through the same position every time a certain period of time elapses.

The same is true for the circular motion, every time the object completes a turn, the object is in the same position.

They are examples of simple harmonic motions. The time it takes the object to repeat a complete cycle is called period.

Therefore, in a grahp of position versus time, the curve that represents the position repeats itself every so often equal to one period, both for moving back and forth and for moving in a circle.