The reason why I think retail investors hold more stocks than investment institutions

I did some research and it seems like some people are saying that most of the money in the stock market is from investment institutions rather than retail investors but that number is based off of AUM. And then I read the following excerpt from an article

"The largest private asset manager is BlackRock, which holds about $10 trillion in assets under management as of 2022. Note that most of these assets are held in the name of BlackRock's clients; they are not owned by BlackRock itself."

So it seems to me that AUM is basically individuals' money at the end of the day and the institutions are just holding the money to provide administrative services or maybe give some "guidance" but the final decision is made by individuals.

Also if I just think about it from a commonsense perspective, \~600 million individuals around the globe participating in the US stock market have more money than a dozen institutions participating in US stock market.

What do you guys think? Is there any reliable source showing that my assessment is wrong?