Kaomoji are probably what you think of when you think of Japanese emoticons. These are text based emoticons made out of a wide variety of different 2-byte characters. Kaomoji means "Facemark" in Japanese.
Emoji are small image emoticons that were invented in Japan for use with cellphones. The word Emoji means "Picture Letter" in Japanese. Emoji are built into a bunch of different cell phones and are standardized across devices.