> When someone replaced :-) with a smiley picture, there was a debate about whether they should be called emoticons or emojis

[citation needed].

The history of the word emoji isn't some mysterious thing - the wikipedia article linked in your parent post has it all laid out.

Emoji is a Japanese word meaning pictograph, it isn't derived from the word 'emoticon'. They were developed by Japanese phone companies as an idiomatic expressive addition to Japanese writing, not because 'someone replaced :-) with a smiley picture'. There was no time when they might have ended up being called emoticons.