What directly causes the pressure difference between the equator and the polls

The primary factor that causes the pressure difference between the equator and the poles is the uneven distribution of solar energy received by the Earth's surface.

At the equator, solar radiation is more intense compared to the poles because it falls more directly on a smaller surface area. This causes the air to heat up, expand, and rise, resulting in the formation of a low-pressure zone. As the warm air rises, it creates a vertical circulation pattern known as convection cells, where air ascends at the equator and descends at the poles.

Conversely, at the poles, solar radiation is spread out over a larger surface area, leading to less intense heating. The colder air near the poles is denser and more prone to sinking, causing the formation of a high-pressure zone.

The pressure gradient resulting from this temperature difference between the equator and the poles creates winds that blow from high pressure (poles) to low pressure (equator). These winds, combined with the rotation of the Earth, result in the global circulation patterns known as the Ferrel Cells and Hadley Cells, influencing weather and climate patterns worldwide.