I've answered this various times in various ways when my kids ask.
"Well, compared to most of the earth's population, yes, we are VERY VERY VERY rich. We live in a house, we drive a car, we have clothes and food and electricity. We travel around and do stuff in a fancy society. We are much much richer than most humans could ever dream of being. However, here in America, we are not rich at all. We have everything we need, and are very privileged, but we work hard, and we do not have nearly as much money as some people. We have to be careful how we spend our money, and there are many things we can't afford. We are what is called "working class or lower middle class" I guess. You kids will need to work hard to establish yourselves and earn whatever you want. We will not have money to hand you educations and houses and cars. But that's for the best anyway, your father and I both made our own way, and you can have and do whatever you want in this world if you work hard enough. We do have much more money than some of your school mates, and it's not nice to brag about money or talk about it to people outside of your own family."
If their father or I WERE rich from a high income or family money, I would tell them, "Yes, we are financially rich by society's standards."
We live near a very elite university where all the students ARE RICH!!!! And I have several friends who teach there. Would you believe that many of the students have been brain-wahsed by their parents to believe they "aren't rich"? It's the most condescending thing ever because they go around saying, "We're not rich, we had to work really hard, nothing was handed to us" VICARIOUSLY through their parents who may have been less rich when they went to college 30 years ago and who have recited that mantra to their kids....who at age 19 drive the newest Range Rovers and wear head-to-toe designer clothes while attending the $70,000/year college....and it makes them less empathetic to people who really aren't rich.