Answer:
It is a similar case, given that both can be modeled as uniform circular motion. The inward force for the Earth-moon case is provided by gravity's force, and in the case of the ball-string it is provided by the tension on the string.
Explanation:
There are parellels between both cases:
in the Earth-moon movement, the mass of each astral body generates a pulling force (gravity) which, given the correct circumstances, makes each object revolve a common center of mass, almost in a circular trajectory. Of course, since we are not in such point in space but standing on Earth, we see as the moon is revolving around the earth. The inward force would be gravity in this case. There are other forces involved such as the pulling on the sun, but it is common to both bodies so it is not relevant in this picture.
The ball swirling around you is possible because it is attached to a rope or string, which constantly pulls the ball towards the center (you). The force involved here is called the 'tension' on the rope. The circular movement is a combination of tangential velocity and inward radial force. There are other forces which are more relevant here, such as the friction with the air and the acceleration of gravity of the Earth on the ball, which can actually alter the trajectory of the ball. The pulling must supply some pushing force to counter those forces.
For more information and insight on this problem I recommend videos on uniform circular motion and centripetal forces.