ol·i·gar·chy
/ˈäləˌɡärkē/
noun
a small group of people having control of a country, organization, or institution.
-a country governed by an oligarchy.
"the English aristocratic oligarchy of the 19th century"
-government by an oligarchy.
ol·i·gop·o·ly
/ˌäləˈɡäpəlē/
noun
a state of limited competition, in which a market is shared by a small number of producers or sellers.
ol·i·garch
/ˈäləˌɡärk/
noun
1. a ruler in an oligarchy.
2. (especially in Russia) a very rich business leader with a great deal of political influence.
So, is Elon Musk an oligarch?
Well, no, I don't think so. People keep using that word; but, I don't think that they know what it means.
There's overlap in the concepts of who can be a part of an oligarchy and an oligopoly. One could argue that Musk is a member of an oligopoly in terms of his supposed immense power; but, that's using the word loosely.
Really, social media was an oligopoly. Social media could be argued to be part of an oligarchy. But, since the members of the oligopoly and the oligarchy seem to be freaking out about Musk, it doesn't seem that Musk is joining the oligarchy and therefore becoming an oligarch. It seems that he's disrupting the oligarchy and therefore not becoming an oligarch.
Again people, words mean what they mean.