I read from this site:
that there are different types of stationarity:
Strict stationarity means that the joint distribution of any moments of any degree (e.g. expected values, variances, third order and higher moments) within the process is never dependent on time. This definition is in practice too strict to be used for any real-life model. First-order stationarity series have means that never changes with time. Any other statistics (like variance) can change. Second-order stationarity (also called weak stationarity) time series have a constant mean, variance and an autocovariance that doesn’t change with time. Other statistics in the system are free to change over time. This constrained version of strict stationarity is very common. Trend-stationary models fluctuate around a deterministic trend (the series mean). These deterministic trends can be linear or quadratic, but the amplitude (height of one oscillation) of the fluctuations neither increases nor decreases across the series. Difference-stationary models are models that need one or more differencings to become stationary (see Transforming Models below).
some types of stationarities deal with the mean and the variance, while others only the mean.
Which type of stationarity does the Augmented Dickey Fuller assess? Does it need both the mean and the variance to be constant, or only the mean and not the variance?