Occultation is the moving of one body in front of another. The Moon occults the Sun during a solar eclipse, the Earth occults the Moon during a Lunar eclipse, and the Moon can occult a distant planet or star as it passes in front of it.
Transit is the passage of one body across the face of a second body.
The planet Mercury can transit the disk of the Sun as seen from earth and appears as a small black spot. A Moon of Jupiter can transit across the disk of Jupiter as seen from Earth. Ingress means that a body has just passed behind a second body or its shadow. For example, the Voyager 2 spacecraft passed behind Jupiter and ingressed its shadow. Egress means to exit from behind a second body or its shadow.