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Transits occur when a celestial body moves directly between a viewer and another more distant object, often a star or planet. Imagine standing in a straight line with those three objects: the viewer, the transit body, and the distant target. When the alignment is perfect, the transit body partially or fully obscures the view of the target.

Transits are most likely when the orbits involved are closely aligned with the ecliptic, which is the apparent path of the Sun across the sky. For a planet like Jupiter, with its equator tilted at just \(3^{\circ}\), the orbits of its satellites align well with the ecliptic. This means transits of the Galilean moons can often be seen from Earth.

For Saturn, which has an equatorial tilt of \(27^{\circ}\), the orbits of its satellites appear more skewed. This makes transits less frequent, as the moons are often outside the necessary alignment.

Eclipses involve one celestial body moving into the shadow of another. Similar to transits, alignment is crucial. When a celestial body like a planet or moon enters the shadow cone of another, an eclipse occurs.

This phenomenon is most observable when the involved orbits are aligned with our view. For Jupiter, its small tilt means that its satellites, including the famous Galilean moons, move often through each other's shadows. The result is frequent and observable eclipses.

In contrast, Saturn's larger tilt causes its satellites to orbit at a greater angle to the ecliptic. Consequently, the moons do not often enter each other’s shadows, making eclipses rare events.

Occultations happen when a foreground object completely obscures a background object. Picture a larger object passing precisely in front of a smaller one along the viewer’s line of sight. The effect is a temporary hide-and-seek game in the cosmos.

Just like with transits and eclipses, the alignment of celestial bodies is crucial for occultations. For planets with a small axial tilt, like Jupiter, the geometry favors frequent alignments. Thus, its moons regularly occult other celestial bodies.

Saturn's significant axial tilt, however, leads to fewer such alignments from Earth's perspective. Its moons, following orbits more inclined to the ecliptic, rarely move in front of other celestial forms perfectly to cause occultations that can be observed from our planet.