Wealth is food, clothes, a house, a car. Money is not wealth, but rather a claim on it.
Yes, money is not wealth on that we agree. However I doubt that owning clothes, car & house truly represents wealth. Say a slave owns his machete & shack - is he wealthier that the one which does not (but has them just the same)? If your boss wants you there 8:00 AM sharp and for that you maintain a house near his factory & have to own a car - are these signs of your wealth?
You do not simply sell yourself to your boss; you
rent yourself to him. During the day of work, when he owns you, you cannot enjoy your wealth without his permission, so it does not belong to you without also belonging to him. After that, or when in vacation, you can freely enjoy your wealth, so it belongs to just you. In other words, your wealth only belongs to just you during the time you do not belong to your boss.
Again, (modern) money aint claim a thing. It used to be claim on gold but not anymore. Most people may volunteer to exchange their goods or services for your money but they don't have to.
Before 1971, dollars were legally a proxy representation of gold. You can say they were a "claim" on gold as long as you remember that both were money: gold was directly money while dollars were just indirectly so. However, although now money is purely debt, it still is a claim on wealth, just as it was before (when people talk about the collapse of the dollar, they are precisely talking about the day the dollar will no longer be a claim on wealth).
However, being able to "extract labor" makes you a capital owner ... having capital is to have the means of producing new wealth and control over the workers needed to produce itYou are absolutely right that capital is about control over workers. However the wealth is not the material outcome but rather the very process by which part of the output is directed towards certain people's needs. For example the daily output of an armaments factory does not represent wealth. But the process by which your can be consistently made to build bombs for the benefit of a tiny ME country & its supporters is wealth.
Wealth is a useful product of labor. So the means of production (machines, commodity resources, etc), which are indirectly useful products of labor (they are useful in producing useful things), are also wealth. However, the
process of production itself is not wealth: it remains the process by which the means of production
become wealth.
Money being a claim on wealth simply means that it can buy useful products of labor (wealth).
Ditto, consumer goods are not wealth. In fact many are waste.
A consumer good may be useless to you, but if somebody else regards it as useful (even if you disagree), then it is a useful product of labor, which is the very definition of wealth.
People can be wealthy without having capital
Damn right. the Kennedy's, the Bush's, the Clinton's - they are all wealthy without owning much capital. So are countless top-level state bureaucrats who could direct the effort of millions to their own benefit. Hence they are wealthy.
Nobody has to be a Kennedy to be wealthy. Even if I am far less wealthy than the Kennedys were, I am still wealthy.
..., by working for money and buying the useful products of their own work and those of the work of other people.
It's true that everyone works. And this is the genius of the system: I work for 8 hours and make $200. Some political pundit earns the same in 10 min explaining on CNN the brilliancy of certain BofA, whose chairman makes $25K/ day and which acts in the interest of an lobby of the top 2% of the us population. I don't agree but I have to pay my mortgage to that institution just the same (claim on labor). So does the pundit. The BofA chairman also works - he makes bets with our money on all kinds of things. When he's right - he gets a bonus. When he's wrong - he gets a bailout with my taxes. Now I have to work extra hard because the school got de-funded and I need to put my kids in a private one which is expensive. And I learn that the private school principal & the BofA chairman share the same culinary taste - what a coincidence!
Now you talk about a "claim on labor" to mean a different thing: a claim on the money you earned with your labor. The fundamental problem with this system - of which the scenario you described is a late consequence - is that the public aspect of money has been long privatized: money has long become debt. For decades now, this has concentrated money (which is ultimately power) in the very few hands of the so-called 1%, and will continue to do so as long as money remains a form of debt.