“Equities perform especially well in real terms when inflation is low” vs “Certain empirical studies have shown that real returns on equities and inflation have positive correlation over the long term” - What is true? How to interpret? - Portfolio Construction

So in Portfolio Construction - Module 4 - pg. 244, it is mentioned that, “Equities perform especially well in real terms when inflation is low.”

In contrast, In Portfolio Construction - Module 1 - Page 6, is is mentioned that, ”Although individual equities or sectors can protect against inflation, the success of equities as an asset class in hedging inflation has been mixed. Certain empirical studies have shown that real returns on equities and inflation have positive correlation over the long term, but the degree of correlation typically varies by country and is dependent on the time period assessed. For severe inflationary periods, such as periods with an annual inflation rate over 5%, studies have shown that real returns on equities and inflation have been negatively correlated. Therefore, the asset class’s efficacy as an inflation hedge may fail when it is most needed”

My rationale for the same was something on the lines of: Lower inflation = lower economic growth = bad for business, Equities would not perform well

If equities perform well in low inflation periods and perform poorly/fail as a hedge in high inflation environment, isn’t there a negative correlation between the two?

It seems like I’m missing something right in front of my face, but I’m not exactly able to get my head around it