Steiner divides the various bodies of the human into the physical body which is simply matter, the etheric body which is a feature of all living things, including plants and is the information field that guides the physical growth, the astral body which is the container of emotions, also present with higher animals, and finally the I which is specific to the human form. This same division is found in theosophy in general and in Western and Eastern esoteric traditions under somewhat different names.
For example, Mark Hedsel in Zelator discusses a system of seven bodies, starting with the 4 ones mentioned above, then continuing with 3 higher ones that correspond to a higher degree of development of the etheric, astral and I. These are called Buddhi, Manas and Atman.
Whether man possesses so-called higher bodies from birth varies from teaching to teaching. Theosophy and anthroposophy for example teach that such exist, although their level of perfection may vary a great deal whereas Gurdjieff says there are no such things except in rare esoterically advanced people. It may be that the difference is more of semantics. Whether something be an unformed blank slate without lasting conscious consistency or simply absent may make little difference.
Gurdjieff teaches that the non-physical bodies exist only in potential and need to be constructed by conscious work. Acquiring an astral body is in theory possible but requires generating and holding large amounts of ‘higher hydrogens.’ This astral body is called the body kesdjan in Beelzebub’s Tales. There is another still higher body which is called soul and is composed yet again of a different degree of hydrogen. There is no separate mention of an etheric body in the sense of a field of ‘life force’ guiding the formation of the physical body.
We can bridge between Gurdjieff and Steiner by the system of seven bodies presented by Hedsel. The 4 first bodies of Steiner, physical, etheric, astral and I would correspond to Gurdjieff’s planetary body. The various functions like biological growth, emotion and thought have their own centers but these are not treated as separate bodies. The higher being bodies of Gurdjieff would correspond to Manas and Atman. In other words, the formation of these would correspond to refinement of emotions and of intellect, corresponding to access to the corresponding higher centers.
The idea is that there exists a higher variant of emotion and a higher variant of intellect. To these correspond bodies which may be developed, or rather which will construct themselves from the appropriate hydrogens if these hydrogens are produced by the lower organism. For example, the transformation of negative emotions can produce construction material for the body kesdjan and later soul.
The ideas of the higher bodies and of the higher centers are not exactly the same. We could say that constructing the higher bodies corresponds to making the higher functioning permanent.
The astral and the next higher body, variously called atman or soul are the only ones that survive physical death. We can only speak of purposeful reincarnation if these bodies exist and have cohesion. Otherwise we may only speak of a mechanical recycling of patterns or of looping of a film.
The Cassiopaea material divides the human into the physical body, consciousness, the genetic body, and spirit/etheric body. The material does not go particularly deep into their functions or delineations. From the context of usage we could infer that the C’s etheric is whatever survives between incarnations, corresponding to Steiner’s I and parts of astral. The genetic would probably correspond to Steiner’s etheric, meaning an information field whose presence separates living from inanimate matter and consciousness would correspond to transient parts of I and astral. Such comparisons are however of little practical consequence.