Origin of the word “Emoji”
The word Emoji comes from the Japanese word “e” for picture and also the Japanese word “moji” for character. So it is a picture character. In English the word “emoticon” is a concatenation of the words “emotional” (or “emotive”) and “icon”. See Emoji at Wikipedia. More emojis are available at https://en.support.wordpress.com/emoji/ than for https://codex.wordpress.org/Using_Smilies, by default.
Examples
Of the emojis available at WordPress.com, which are available for WordPress.org, I found the following (please ignore the quote marks):
“:)” gives 🙂 , “:-)” also gives 🙂 , “;)” gives 😉 , “;-)” also gives 😉 ,”:D” gives 😀 ,
“:-D” also gives 😀 , XD Does Not work, >:D( Does Not work, :'( Does Not work, “:|” gives 😐 ,
:/ Does Not work, “:o” gives 😮 , “:P” gives 😛 , “:(” gives 🙁 , >:( Does not work, o_O Does Not work,
“8-)” gives 😎 , ^^’ Does Not work, <3 Does Not work, “:?” gives 😕 , =^-^= Does Not work
“:evil:” gives 👿 , “:twisted” gives 😈 , “:mrgreen:” gives 
, “:oops:” gives 😳 , “:roll:” gives 🙄 ,
“:idea:” gives 💡 , “:?:” gives ❓ , :bear: Does Not work, :star: Does Not work, “:arrow:” gives ➡
There may be others 🙂
You can make the emoticons larger by putting them in a heading. In your WordPress Dashboard, highlight the characters in the smiley, select the paragraph drop-down arrow, and then choose the size of heading you require:
🙂 Heading 1 size
🙂 Heading 3 size
But it does then have to go on a sperate line to the rest of your text, otherwise that will be heading size too.
Emoji and Emoticon Plugins
Of course there are plugins available to enhance the available icons available to you. It seems that if you search for emojis and then emoticons then you get different choices of plugins 😮
Unicode
I will put the following in a seperate post some time but you may want to use Unicode as well as emojis. Two excellent sites for examples are http://tutorialzine.com/2014/12/you-dont-need-icons-here-are-100-unicode-symbols-that-you-can-use/ and https://www.w3schools.com/charsets/ref_utf_symbols.asp. Don’t forget to start with &#, for the decimal version of the code or &#x for the hexidecimal version. Also remember to put a semi-colon (;) on the end. You just put it in your html code and the symbols show on your website, cool. ⛵