Khat - the physical body
This is the material self including the body and brain. It is what limits consciousness and binds it here. Early on the Egyptians did not find as much value in the bodies as they later came to. Wainwright talks about how the early kings and other royal/religious figures were cremated and used in rain making rituals. Early burials at Nubt were not mummified and sometimes left rather exposed, and in other instances their heads were removed and faced opposite their body. It was only with the coming of the Agricultural Tradition that the body became important. The body is not the creator nor receptor of consciousness, but rather a limiter of it. I would argue it was a terrible mistake to obsess so much over the material body.
Ren - the name
In otherwords, what a thing is called, the thing in itself. This is not just the birth or defining name for someone/thing, people and things could have any number of names in Egypt. Many still do today. I think a good comparison might be identity, what the outward world sees, how one presents themselves to it. Honestly the birth name may be misleading, it is given without any input from the inividual, and surely names one chooses to take for themselves are far more meaningful.
Shut/Khabit - shadow
Not only the literal shadow, but I think we can understand this as the Jungian shadow as well. The opposite of the outward labels, the shadow is often hidden even from the individual themselves. It could also be considered the subconscious, the untamed abyss of the mind. The deepest fears, biggest secrets, everything hidden away from the world and often the self resides here. If it is neglected enough perhaps the Khabit can become its own force and leave behind a nasty presence, or be sent out by the individual.
Ib - ego (heart)
The Egyptians generally believed the soul resided in the heart. If they existed today it would probably be the brain, but we are smart enough to know the mind was not created by the body, irrelevant of which organ. The ego is the connection between the physical and immaterial worlds of the body and soul(s) respectively. It is the ego of a person that was weighted in the halls of Ma'at, at least imo. It is the immediately conscious aspect making choices in real time, directly interacting with the external world via the Khat. The ego-consciousness, to riff off Aquino, is the field generated by interaction of the limiting brain with the infinite soul.
Sahu - the astral / spiritual body / ghosts
I think the concept of a spiritual body is mainstream enough to avoid diving in too deeply. It is a "body of light" but not the soul in and of itself as we would normally use that term. Similarly it can be compared to the Life and Thought Fields of Dr. Burr and Ravitz. It is what can create an inner temple while still bound to matter, what can journey out and speak with spirits/the gods, and so forth.
I personally theorize two types of ghosts: "glitches" and "hauntings". A glitch is your normal ghost: same places, same times, triggered by the same events, and so on. It does not seem to have will of its own. This is the glitch, someone either "stuck" or simply an accidental overlapping in space across time. A haunting, with intent, is either a malevolent Shadow (Khabit) or the remaining body of light of a dead and/or enlightened entity - a way to perhaps still interact with this world, if in a severely limited capacity.
Ba - self awareness / personality
The "I" in "I exist". You, me. The infinite center, the ultimate axiom, the individual themselves. It is limited by the brain now but is, in reality, infinite. It undergoes "Anamnesis". When one goes into sensory deprivation tanks they do not go unconscious, the mind expands outward, theoretically infinitely. A lack of oxygen in a dying brain should provide only darkness and confusion, not crystal clear, often consistent phenomenon of consciousness expansion. Death is not the end, at death your Ba (symbolized by a human headed bird in Egypt) flies off onto other things - be it reincarnation, entering the realm of a deity, merging with a deity, or deification. Nor is the body at all necessary for it, or more than a prison - something only the earliest Egyptians, such as at Nubt, recognized.
Ka - divine spark
Being itself, the "divine spark". As independent as one may become, this itself is reliant on there being order to chaos. Do not think that the material world of horrors is all that exists of order, Set may oppose both chaos and the demiurge but upholds Ma'at! There is a difference between utilizing order (non-chaos) for one's own purposes and being slaved to the order of someone else. The Ka is why the individual and patron deity are a reflection of each other, and it can be considered the Platonic Form of the individual.
Beyond these 7 parts of the soul, there is a final stage that can be achieved:
Akh - deification
This is apotheosis, self-deification, the self separating from all order and creating its own as seen in the Pyramid Texts, a man or woman becoming equal to the gods, or even greater.
"(N) leads the gods, he directs the divine boat. (N) seizes heaven, its pillars and stars. The gods come to (N) bowing, and the spirits escort (N) to his soul. For behold, (N) is a great one, the son of a great one, who Nwt birthed. The power of (N) is the power of Set in Ombos. (N) is the great bull who comes forth, the pouring down of rain. (N) comes forth as the coming into being of water, for he is the Serpent with many coils. (N) is scribe of the divine book who decides what exists and what ceases. (N) is stronger than men, mightier than the gods. Horus carries (N), Set lifts him up."
The Pyramid Texts