I see the difference between "manifestation" and "form" being this. "Form" is a physical presence, for instance a statue, or the form of another god where both gods are in fact one, or many. Sekhmet-Hathor being an example, or maybe Wepwawet being a form of Anubis, or vice versa, but that's another discussion. "Manifestation" I see as the ba of the god becoming manifest in a form, such as a statue or a sacred animal such as the Apis bull or the falcon at Nekhen/Edfu. So, for instance, in the case of Sekhmet-Hathor we have two forms, the woman-lioness and the woman-cow, but both containing a manifestation of what is one god, and which is the "upper tier", Sekhmet or Hathor is debatable. But here we can go into manifestations of Ra and where Aten fits in, and is he a separate god or not. So while we can debate whether Sekhmet or Hathor is the original goddess, both are really manifestations of Ra. Here we can be led astray by the Egyptians need to make their cosmology understandable and so use terms such as Sekhmet being the daughter of Ra, because that makes more sense to the majority than engaging in lofty esoteric discussion that will pass right over the heads of the peasants in the fields. We live in family groups, therefore the gods had to, for simplicity if nothing else.
Leaving out Atum, Amun and Ptah, as it just gets too complicated, Ra, in the context of this discussion about Akhenaten, is God, his real name and form are unknown to us. The Sun is a form of Ra as it is a physical presence and has the ba of Ra manifest within it, but it is not the totality of Ra as at night it has gone, died, and Ra is seen by the Egyptians as being in the form of a man spending the next twelve hours battling demons and Apophis before becoming joined with Osiris and reborn as Khepri/Horus the Younger/Ra-Horakhty. So Ra is all his forms and manifestations all of the time, whereas the Aten is only a part of this totality of Ra, and while it was always known that the light of the Sun gives life, to deny the existence of the Duat, and so Osiris, denies us the possibility of resurrection. For Egyptians these two aspects of Ra cannot be unbound. They could see the Sun "die" at night and be resurrected at dawn, and for them there has to be a mechanism for this resurrection, as explained above. The existence of Ra implies the existence of the Duat and of Osiris, therefore Ra, as Ra-Horakhty, was eventually ditched as he was incompatible with Akhenaten's idea of there being one god, who is only the visible Sun. This, IMO, goes back to the times of Khufu where there was, as far as is known, no Duat, no Osiris and no hope of resurrection for anybody except the king, these things came later, at least in the form we are familiar with. So, at the end of the day, the Aten is a part of a broken Ra, not, for anybody except Akhenaten and his acolytes, a properly functioning god, let alone God.
A discussion of where the other gods, such as Thoth, fit into all this, and are they manifestations/forms of a higher god or autonomous is a discussion of the "One and the Many", and would need a separate thread, with the potential to be far bigger.