Emote
An emote is a small picture that resembles an emoji but doesn't have an actual Unicode codepoint.
Most emotes are triggered by using a phrase or shorthand. For example, the PogChamp emote on Twitch.tv can be used by simply typing "PogChamp". Instead, a shorthand would look like ":smile:", which would also be used by typing the shorthand including the colons.
Although they are commonly referred to as emojis, emotes are technically not emojis.