Edit: this math is bad, see sokoloff's comment below.
https://www.investopedia.com/terms/r/real-value.asp
A year showing any growth in real terms is a nominal growth that is higher than inflation.
That being said, there's definitely a disconnect. The CPI metric is constantly changing, and is such a broad economic indicator that many people's experiences will not "feel" like what the federal data suggests.
The root of the growing wealth gap is the massive deficit we've been running. Especially since the GFC, the strategy has been to rack up a bunch of debt and inflate that debt away. This inflates the value of financial assets, property, and commodities...none of which is owned by the average joe whose cash savings gets destroyed in the interim.
> none of which is owned by the average joe
About 66% of US households "own" a home (often with a fixed-rate mortgage, which makes rising inflation doubly good for those homeowners) and 58% of homes are owner-occupied. The median Joe is a homeowner, not a renter.