This is an extra piece of information.
emoji are the picture icons. You are correct. And ":-)"-like faces are "Emoticons", as RexYuan answers.
Some of the other punctual faces are technically "dongers" or "kaomoji" depend on what characters they are made of. Dongers usually have thinner strokes like ᕙ༼ຈل͜ຈ༽ᕗ , while kaomoji characters are less gnarly e.g. (╯‵□′)╯.
Since the term "emoji" is better known, people might refer it to as dongers or kaomoji. It could be picky to argue the terminology under some circumstances.
Hope this helps.