Aset and Hethert were not equated with each other in ancient Egypt. Many goddesses, not just Aset, wore the horns and sundisk headdress. This did not equate them with Hethert (Hathor). Sharing attributes is common among Kemetic gods and this does not mean that these gods have the same identity, just a same or similar sphere of influence.
Within a Kemetic context Aset and Hethert are different deities and both differ from their Greek/Roman re-interpretations including their myths, personalities and attributes.
According to Sigfried Morenz in his book, "Egyptian Religion", Hathor/Hethert was identified with Isis/Aset (I prefer the Greek names because I think they are closer to how they would have actually been pronounced, as Egyptologists use the letter "e" as the default vowel when reconstructing the words). The book isn't perfect, but I think he's right about that. Many books say that evidence suggests that Hathor was originally the mother of Horus/Heru in the story of his conflict with Seth. When the Isis/Osiris (Wesir) cult became associated with Horus and Seth, Isis is believed to have taken Hathor's place as the mother of Horus. It's just a theory, but I think it's a valid one.
Isis originally had the throne headdress, presumably until she merged with Hathor because of shared characteristics. Isis had the title "lady of heaven", which probably came from her association with Hathor, since Isis probably did not originally have sky associations before being identified with Hathor. Also, one hymn to Hathot I can think of says this: "You from whom the Divine Entities come forth in this Your Name of Mut-Aset!", identifying her with both Mut and Isis as a syncretic deity (
http://www.hethert.org/hymnsprayers.htm#Hymn%20from%20the%20Temple%20of%20Heru%20at%20Edfu).
Isis and Hathor are distinct goddesses, but like many Egyptian deities, they could be identified or merge with each other, like Ra could with Horus, Amun or Atum, Hathor with Sekhmet, et cetera. Hard polytheism is not a good way to understand Egyptian gods, as evidenced by things like the above hymn.
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