If you look up the word "frugal" in the dictionary, the definition has no relationship to income, only spending. And in today's world spending doesn't even have a strict relationship with income because of all the debt services available to people. What you see is people with means being frugal by choice, whereas some folks may be frugal by necessity. Both are possible.
I looked it up as I never really thought of the actual definition. So according to Merrian Webbster:
"Definition of frugal: characterized by or reflecting economy in the use of resources".
That's probably many people here both during there working years and during retirement with regard to money. And of course many are "frugal" in their use of other kinds of resources beyond money. But I think the OPs definition falls flat overall. Is Jeff Bezos frugal if he doesn't spend a million bucks a day if that is what his income would allow? Is some here who chooses to live on little and FIRE young NOT frugal if they are spending their whole $1000/month passive income?
It's both really.
That's why this thread is so silly.
I consider some very wealthy people who live like upper middle class people and very thoughtfully so to be very relatively frugal considering their spending capacity. But I also consider the leanFIRE person who is house hacking and dumpster diving to live their dream to be frugal as well.
Anyone who intentionally, and thoughtfully tries to spend very carefully and stretch their dollars is frugal.
So for example, I know a lot of wealthy people and some live well below their means but still aren't very frugal. They just never inflated their lifestyle past a certain point, but they're still wasteful and careless with their spending. Still heavily consumerism driven, just not upgrading their consumerism to a more expensive level. So having a room full of purses, but they're all $2-3K Louis Vuitton instead of $50-60K rare leather Birkins.
I don't consider someone frugal because they have a room full of expensive purses just because they can afford a higher end of ridiculous consumerism.
But I also know very wealthy people who don't spend even a fraction of what they could and when they do, they're very thoughtful about their spending. They might spend a lot on clothes, but specifically try to support local environmentally driven designers. They might use their purchasing power very carefully and only spend when it aligns with their values. They're frugal in a relative sense where it's all about less consumerism, and getting the most for their dollar, but for them the biggest part of "the most" is the impact, not just how the consumption benefits them.
Then there's the ultra rich cheap bastards. They're the most amusing. They're miserly fucks who cling to every cent as hard as they can. They spend the least and the only joy they get from their money is having it and watching it grow. For Christmas, they give their family the free gifts they get at department stores.
They're not frugal, they're cheap. I'm related to one, it's a delight.
On the other extreme, there's the family living on next to nothing, barely scraping by. The frugal version is meticulously careful, making everything last and stretch as long as possible. But the non frugal version has just as little money to survive on, but prioritizes buying cigarettes and beer.
So it's not so much that frugality is a specific level of living below your means, it a specific level of spending. It's more that frugality is the antithesis of wasteful consumerism.
So when you frame it by what it isn't, it becomes clearer what it is.