I don't know if there's really a metric to measure the difference between rich and wealth. Because when discussing finances, they're kind of two different situations. I suppose if you're wealthy, you're in a position to make trusts and pass down the majority of your funds and property into generational wealth, or to maintain a family business or legacy. Much of your money is not immediately available, but you can still live without worrying about the price of things you want to buy or do, or handling emergencies.
Being rich just means you have enough money you can spend on whatever with the minimum of worry about how much much it costs.
There still needs to be a basic monetary value to set as a baseline - say, being a member of the top .05% income or asset level.
My thought is that wealthy person could be someone who is happy living relatively frugally, but, including assets, might only be just be considered in the top .05% to be able to be disbursed to heirs. Or has over half their wealth in a business or some investment that is not very liquid within the financial baseline set up in the premise.
A rich person might be in the top .02% with mostly liquid assets (or easily accessible assets), but could very well be spending their way into eventual bankruptcy by the end of life.
My FIL was rich, but not wealthy. The money in his trust that will come to my spouse and his sister when each turns 65 pretty much is there for each to pay off any lingering bills and pay for a couple vacation trips - or a decade or so in assisted living or a nursing home if needed.
But all of this is just my opinion. The economic study/dictionary definitions of wealthy and rich I've seen are pretty subjective and interchangeable.
Haele