And Emoticon is a combination word resulting from "Emotion" and "Icon" --- therefore, it is an icon depicting an emotion.
And I've just figured the word "Emote" was a shortened version of the word "Emoticon". Since people refer to "emotes" in the plural sense (implying that "emotes" are ALSO icons that depict an emotion), I've just assumed the two words were synonymous.
...I suppose it could also be a verb, though ("to emote").
I beleive a Emote and Emoticon are the same. As they both are forms of Art that reflect a emotion of action that the Emoticonist tries to reflect upon their audience. To show them how they feel and/or what they want their audience to feel.