All it really is is a different romanization system. Compare Hepburn and Shin-Kunrei-Shiki. Hepburn would say Kannazuki and Shin-Kunrei-Shiki would say Kannaduki. I personally prefer Kannadzuki, since that's how I used to type the "dzu" character with IMEs...but recently I just find that z or "s" in "tsu" to be a pain and so just do "du" or "tu."
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I do know Himeko/Chikane make a suggested 'reincarnation cameo' in an anime by the same maker.
I suppose you could say that, but they do have more than a "cameo" appearance in the anime (called Kyoushirou to Towa no Sora). Kaon ("Chikane") has more of a part than Himiko ("Himeko"), sort of, but they still appear more than just once or twice. I recommend watching it, though it might not have the same wow factor as Kannadzuki no Miko. I like it.
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Back when I got into Yamibou everyone compared the two and said the characters were similar.
Other than the fact that Chikane sort of looks like Hadzuki and Himeko like Hatsumi, I wouldn't compare them
too much. Hadzuki's somewhat...nicer than Chikane, to say one thing. She also seems less refined and not quite as talkative. Or...something. I don't know. XD
"Do you see anything? It seems to me I am trying to tell you a dream - making a vain attempt, beceause no relation of a dream can convey the dream sensation, that commingling of absurdity, surprise, and bewilderment in a tremor of struggling revolt, that notion of being captured by the incredible which is the very essence of dreams...."