Many, many people choose to appear rich. This usually means buying a house you can't really afford, cars you can't really afford, and all sorts of electronic devices and jewelry and other items that you can't really afford. Outwardly, you appear to have lots of money, but you're actually sinking in a giant pile of debt, barely able to keep your head above water.
In this case, the appearance of affluence doesn't equal financial independence. Instead, it equals a huge amount of financial dependence. People in such situations depend on their employer for steady employment. They depend on their continued good health. They depend on minimizing major unexpected events.That's far from financial independence. But from the outside, it does look good.
On the other hand, one can choose to be rich. From my perspective, being rich means being as financially independent as possible - almost no life events can impact your situation - and being surrounded by the things you care the most about.
Yes, this has one disadvantage over appearing rich: you don't get lots of shiny things whenever you want them. But it comes with tons of additional advantages.
You're not tied to your job for purposes of compensation. If you hate your job, quit and find something you don't hate. The money isn't the constraint.
You're not buried in bills. Each month, you don't have to pay much at all out in required bills.
You don't have tons of different things that need constant care and maintenance. You're not cleaning a 6,000 square foot house. You're not caring for five different cars. You're not keeping up an immaculately landscaped yard. Sure, if you're passionate about one of these, you can chase it - but if you don't care, there's no need to have them or maintain them at all.
You don't have "friends" that constantly judge you based on the stuff you have.
You don't worry about having enough money when you retire.
In the end, it comes back to one simple question: do you want to appear rich, or do you want to be rich?