Being rich or wealthy is having the ability to change your area by simply stroking a check.
Lots of people who have money can't do that, however. Some can't do it because they have no control over their cash burn rate. Others can't do it because they lack discipline or education or sanity. Five Million Dollars does the flake in the sanitarium no good as he crawls on his knees and barks at the guards, after all.
On the other hand, the programmer who moves to rural India after saving a mere $50,000.00, can employ hundreds of workers to build gravel roads and wood bridges and little grass huts and take out one ad in a travel magazine for a back-country tourist trap.
Ditto for the California couple who sells their tiny Long Beach 2 bedroom hovel for 2 million Dollars and moves in to rural Arkansas or down to Panama. Suddenly that working couple can live like retired kings, employing gardeners, maids, nannies, and building up a local church that names its new daycare building for them.
But the lotto winner, baseball star, and rapper who have no control over their daily spending aren't rich, simply consumptive. Many a jazz star and lottery winner has had to file for bankruptcy, after all, without even so much as a building or a song being named after them.
So being truly wealthy requires more than just cash, at least in my book...and even the amount of cash required will vary relative to the amount of money nearby.