I've added 'in classical physics' in the thread title because all the differences between them that I found on the internet involved relativistic physics. It was something like both momentum and kinetic energy being components of a four-momentum or something like that. But I cannot understand those concepts. These two quantities were defined before there was any relativistic physics. In classical physics, both of them are a quantitative way to express the amount of motion contained in a body. So, I need an intuitive explanation of why do we need to define both of these two quantities.