A stretched catapult has potential energy

No

Explanation:

The potential energy is associated with bodies that are above a reference point, at that reference point the value of potential energy is taken as zero. For example, if an object with a mass M is in a tower that is 140 meters high, its potential energy is defined as the product of the mass of the object by gravity and by the height at which the object is measured from the reference point.

Ep =m*g*h

When talking about elastic objects such as springs or elastic fibers, it is usually understood that there is an elastic potential energy associated with the constant of the spring. This can be calculated using the following equation:

where:

k = elastic constant of the elastic material [N/m]

Dx = distance stretched or compressed of the elastic material [m]

U = elastic energy [Joules]

So, there are differents between the elastic potential energy and the potential energy