I think the main difference is that aristocracy was zero sum and rent seeking where billionaires aren’t necessarily (and with recent tech ones not) zero sum. Bezos having a billion dollars doesn’t limit anyone else from having a billion dollars.
Only the king was allowed to hunt in the king’s forest. Aristocracy owning 50% of land (or whatever) means no else could own it and more land wasn’t (usually) created.
If someone is king, then that means no one else can be.
There’s some similarities with aristocracy, especially with generation after generation. But theoretically we have estate taxes and laws against perpetuity that help some and could be prevented.
Perhaps half of billionaires are “self made” [0]. I don’t like that term, but I wish we had “how many billionaires weren’t born to millionaires?”
But Bill Gates being born to a middle class lawyer and making billions is very different from Bill Gates being born to the Earl of Orkney and selling all the potatoes in Ireland to make billions.
[0] https://www.cnbc.com/2019/05/10/wealthx-billionaire-census-m...