To remove non stationarity in a time series, we can standardize the time series by subtracting the mean and dividing by the standard deviation. We can also keep differencing the time series until the correlogram indicates that the non stationarity has been removed.
Intuitively, I am not able to follow how these two methods that are so completely different are able to produce the same end result. Can these methods be used interchangeably ? Which method to use under which situation ? The differencing method seems better in that we can keep taking differences until the non stationarity is removed, but for standardization , what to do if standardizing does not remove the non stationarity?