Of course, one could argue that since the word is now being used internationally, it's not necessary for them to be interpret in the same way as its roots.
Emoji is a Japanese loan word 絵文字 (literally picture character), you can read more about them:
https://en.wikipedia.org/wiki/Emoji
Emoji in English can used as a singular or plural word but you can also write emojis.
Emoticons are then usually made up out of multiple ASCII-symbols, although general Unicode is by now also in use: :), :-), :|, :[ ...
And then for the "ㄟ(ツ)ㄏ"-Emoticon, you can get more specific about it and call it "Kaomoji". Kaomoji are not Emoji, even though the two sound related, and are actually a more horizontal style of Emoticons, so basically any Emoticon which you can read without turning your head: ㄟ(ツ)ㄏ, ^^, (っ´▽`)っ, (╯°□°)╯︵ ┻━┻, ఠ_ఠ ...
Multi-character ones would be called smileys, emotes, or emoticons. The confusion comes from the fact that many messengers will automatically replace multi-character emotes with an emoji.
Emoticons predate Unicode and emoji, but were later adapted to include Unicode characters.