What is the difference between elastic and inelastic collisions?

For an elastic collision, the total kinetic energy before the collision (ie the sum of the kinetic energies of all the bodies participating in the collision) is equal to the total kinetic energy after the collision. sum of Ek of all bodies after collision). That is, Ek initial = Ek final, where Ek = 1/2 mv^2.

For an inelastic collision, the total kinetic energy before the collision (ie the sum of the kinetic energies of all the bodies participating in the collision) is not equal to the total kinetic energy after the collision. sum of Ek of all bodies after collision). That is, Ek initial not equal to Ek final, where Ek = 1/2 mv^2. In general here, Ek final < Ek initial. This does not violate the Law of Conservation of Energy, since, although Mechanical Energy is "lost" from the system, it is converted into an equivalent amount of other forms of energy, eg heat, sound, light, deformation, etc.

Important to note is that in both cases, elastic and inelastic collisions, momentum (p=mv) is always conserved, irrespective of the elasticity of the collision.

In real-life, all collisions are inelastic. For an example of an elastic collision, you may consider the collisions of the particles of an ideal gas - they are elastic by definition. However, the ideal gas model states that the particles of an ideal gas occupy no volume which is a theoretical thing, hence an ideal gas does not exist in real life, and so the closest approximation to an ideal gas is Helium since its particles are the smallest, and hence the closest you will get to an elastic collision. (Not hydrogen since, even though having less electrons than helium, the covalent bond in the diatomic molecule takes up volume, causing the overall particle size to be bigger than helium and hence further away from ideal gas properties.

In elastic collisions, kinetic energy is conserved, while in inelastic collisions, kinetic energy is not conserved. In elastic collisions, both momentum and kinetic energy are conserved, while in inelastic collisions, momentum is conserved but kinetic energy is not.