Each of the four worlds interacts with the other worlds. Psychic energy flows from the spiritual to mental to astral to physical. Our center of consciousness is generally within these higher worlds. There are many similar terms used by other occult groups. For example, 'astral light' is another name for astral world, although it may sometimes also refer to the entire non-physical realm, as may 'inner planes' or 'the invisible world'.
Planes are essentially the same as worlds.
Vehicles or sheaths are the same as bodies. The 'causal body' is the upper 'mental'. The magician, as a microcosm is thus connected with the macrocosm. There is an intimate relationship of energies between you and everything else. The universe is reflected within us and we are projected into the universe.