Ah my favorite false cognate isn't here, that means I get to post about it!
Emoticon :) is emotion + icon in English, invented in the 80s or early 90s. Exactly what you think.
Emoji is Japanese 絵文字 which basically translates to "picture character". That word has been around for a long time; I don't know that I can put a date to it. But certainly a lot older than computers.
They just happen to sound similar
The fact that me and a coworker can't both share our screens at the same time is absolutely batshit. 1x1 collaboration isn't even reasonable, nevermind anything more