A moving ball primarily has kinetic energy (motion).
Elastic energy comes into effect if the ball is compressed or stretched, like in the case of a bouncing ball.
Theoretical problems usually have perfect pr controlled conditions, but a moving ball in real life would be compressed or changing with its contact with the ground.
If you want more help or could provide more context, feel free to ask.
If this is a question on a test or quiz and its asking what type of energy a 'moving' ball has, generally they want you to think about what causes the movement (in this case, kinetic), because there is always a lot of other energy being transferred and happening at the same time (i.e., thermal, sound).