Think of a light bulb as a small bicycle and a geyser as a heavy-duty truck; while both use the same road (voltage), the truck requires much more fuel (power) to move its weight and perform its job.

The power rating ($P$) of an electrical appliance is the product of voltage ($V$) and current ($I$). Devices that perform high-energy tasks, like resistive heating elements in geysers or heavy-duty compressors in ACs, require a higher current flow, resulting in higher power consumption. This relationship is governed by the formula $P = V \times I$. Appliances with higher power ratings are designed to handle higher current loads to perform their respective functions.

Remember that in a parallel circuit (typical home wiring), all devices receive the same voltage, so the difference in consumption is strictly based on the current they draw to satisfy their power requirements.