To use a boxing analogy, I look at money as one's ability to DELIVER a punch. Wealth is the ability to TAKE a punch.
So, I have a net worth of about 450,000. So we can dole out a 450k punch.
Wealth is the answer to the question: If a catastrophe were to occur to your net worth, how able would you be to bounce back and rebuild.
Here's my wealth:
Education: I have a math degree and a teaching certificate, and I'm a PTR certified high performance tennis instructor. My wife is close to a PHD in ESL and has a degree in spanish. So, if we lost all our money tomorrow, we have lots of power to earn more money quickly and in many ways.
Soft skills: We can cook. We can fix things and are willing/able to do things ourselves. We have grit, ambition, we aren't afraid to fail, etc.
Health: We are very healthy.
Family/Friend: We have lots of family who could and would help us in a time of need, and we have built up lots of connections in our community. We could use these connections if we needed to get a new job or wanted to start a business venture.
Money skills: We know how to invest/save/seek out opportunities/avoid scams.
You could take away our money and we would quickly bounce back over and over again. We are very wealthy.
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Now compare this to many lottery winners, or many professional athletes. They may have a few million dollars, so they have MONEY. They can deliver a massive punch. But most of them have little wealth. They lack the skills/connections I mentioned above, so they quickly lose their money and have limited means to make more money when the well runs dry. This is why so many lottery winners/pro athletes go bankrupt quickly IMO. They can deliver one hell of a punch, but can't take one.