In my opinion, LHP and RHP cannot be defined abstractly, in terms of just one aspect of the principles or aims of a particular path. Instead, I regard LHP and RHP as groupings that have evolved spontaneously, and whose meaning is mainly social and historical.
The cold plate causes the moisture in the warm air, which is inside the jar to condense and form water droplets. This is the same thing that happens in the atmosphere. Warm, moist air rises and meets colder air high in the atmosphere. The water vapor condenses and forms precipitation that falls to the ground.
Warm air has more water vapor than cold air, which is why it is often humid in the summer. Warm air rises, and with it rise the water droplets. These tiny drops rise if cold air blows in. Mountains can also make them rise, which is why it rains a lot there. When the air holds lots of water droplets, clouds form.