The etymology of emoji ought to be obvious. It's a little digital picture: hence e- like e-mail. And it expresses emotion: hence emo-. Except that that's not it at all.First, the OED mentions that the word dates, in Japanese, back to at least 1928, when computer graphics were not up to much. That also means that it's got little to do with e-things or emo-things. E here means picture in Japanese and moji means character. So it's a pictograph, indeed emoji may have originally been a straight Japanese translation of the English word.
Emoji is therefore closely related to Kanji, which is the Japanese writing system that uses Chinese characters. Kan = Chinese and ji = letter.
(So far as I can tell moji and ji are the same, but I don't speak a word of Japanese, I am simply relying on the clever people at the OED, who, I suspect, do.)
Emoticons, on the other hand, are emotion-icons and have been recorded since 1988. They are therefore utterly unrelated to emojis.
And this is from a Japanese picture scroll, or e-makimono, or emaki.