It can be privately held by vanguard/blackrock. The difference is only based on how the "shares" where bought/sold. The "usual" way is to buy shares available on public and formalized markets like stock exchanges.
So what's you say about Tesla and Elon Musk is like Amazon and JB: they are share holders, but not big enough compared to Elon Musk in Tesla (did not check that) then they cannot setup their ppl on management like their CEOs. This is the same with amazon: JB is in control, but vanguard/blackrock are just behind (and azure), namely once JB sells enough of his shares, vanguard/blackrock get in control and then will setup their ppl as CEO and management (unless azure interfere).
Like alphabet(google)/microsoft/apple/starbucks/etc.