The intuitive difference is mostly between the many and the few. Between the ordinary people and the elite. If your money comes from many small streams, it looks likely that many people have independently determined that what you are doing is valuable. If there are a few large streams, the situation is less clear. Maybe your contributions are genuinely valuable, or maybe someone is picking favorites or choosing winners in advance. From that perspective, capital is a poison that permanently puts the reasons of your success in question.
If anything, I remember when the U.S. Senate Appropriations Committee was picking favourites - and that favourite was ULA. Elon gave them hell.
No. Earned income is salary, and taxed as such. Unearned income is capital gains, exercised options, etc, not taxed as income. It's pretty easy.
If we just use this tax office definition, it's effectively impossible to earn a billion dollars because you'd need to pay yourself ~$1.6 billion dollars in salary (depending on where you live), and very, very, few people can afford to do that
The wealth controlled by a startup investor becomes earned income, in your words, when the founder receives pay for their work, in the form of cash or exercised options or whatever else.
To get that earned income, which is derived from wealth but is not the wealth, they have to earn it in the same way the wagies in your first paragraph earned it. The investor (on the board, presumably) has to vote him in as CEO and approve his pay package.
And just as retail customers don’t give their money away for no good reason, neither do investors.