If a light body moving at some speed $v$, collides with a heavy body at rest and shatters on impact, then what type of collision is this? Since the light object breaks into pieces, there must be loss of energy in the form of sound or something, so it can't be an elastic collision. So, is it inelastic or completely inelastic?
Also, will this be any different if the object doesn't break completely, say only the tip of the pencil is broken?
Any fracturing makes the collision inelastic. Some of the kinetic energy had to be used to break the bonds holding the material together (increasing the internal molecular potential energy).
A completely inelastic collision is one where the maximum possible amount of kinetic energy is lost consistent with conservation of momentum. An example would be if the light object collided with the heavy object and the two continued on stuck together. Another example is if an object collides with and sticks to a wall. (Technically the object together with the wall/earth moves for conservation of momentum, but the movement is infinitesimal).
Hope this helps.
