I'm doing my Physics homework and I have a quick question, What is elastic energy and how is it different to kinetic energy?

To understand this, let's look into the atomistic scale of a material. Here you have an array of atoms with the material. Each of the atoms is connected with one another through intramolecular forces (such as ionic bonds and covalent bonds). Now if you stretch the material by applying a uniaxial tensile force, this will stretch the bonds within the material. As a result, some form of energy is stored within the materials as work is done. When you release uniaxial force applied on the material, these bonds will be unstretched and energy will be released. We call this as elastic potential energy. And if you plot out the extension-force curve of this material, the area under the linear-elastic regime of the material is the elastic potential energy. And it is given by U=1/2Fx, where U is the elastic potential energy, F is the force applied and x is the extension of the material. Kinetic energy is acquired when a body of mass is moved with a certain velocity. And this this given by E=1/2mv^2.