Is affluence determined by assets accumulated or income?

Is affluence determined by assets accumulated or income?
Added (1). Rich is a very subjective term. UBS (a company I ironically interned for) surveyed households with a net worth of $1m-$5m and 28% of them consider themselves rich. My family is in an odd situation. A million dollars excluding primary residence was mentioned to be the minimum amount to be considered an accredited investor by SEC standards.
Added (2). In terms of assets we fit the criteria but I like to describe our situation as asset rich but income poor. Our primary residence has a market value of $1.7M and our rental properties total a value of $2.45M. There is no mortgages on all properties. We have investment portfolio with a market value of $800,000. Although we exceed the million dollar mark a majority is not really liquid. Real estate takes awhile to liquidate.
Added (3). The problem with our situation is we do not generate 6 figure incomes. My father passed away and my Mom does not work, the revenue generated from the rental properties cover our expenses. I am also income poor, its ashame that my first job after graduating college is being a teller for a federal credit union. The pay is very low but atleast the benefits and health coverage is very good.
Added (4). We live very comfortablly but on a budget. Most of the things we buy such as clothes are from affordable luxury retailers on the clearance racks or out of season designer clothes from outlet malls. We try to buy everything on sale and we still clip coupons.

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