Allan variance, $\sigma^2[ \tau ]$, or its square root (Allan deviation, $\sigma[ \tau ]$) is a quantity (as function of parameter $\tau$) which is said to be a measure of (or related to) "stability of clocks".
For a recent example cmp. "First accuracy evaluation of NIST-F2" (T. P. Heavner et al.), especially
"Figure 1. The Total deviation (TOTDEV) of NIST-F2".
Clearly, this quantity is referring to one clock itself; e.g. "the NIST-F2" in the article.
However, the Wikipedia page points out that for "practical measurements":
Likewise, the article on the NIST-F2 states that
"The measurement was made using a commercial hydrogen maser as a reference."
With two clocks being involved, there's necessarily concern about clock drift; indeed:
"[...] drift will contribute to [the raw] output result. When measuring a real system, the linear drift or other drift mechanism may need to be estimated and removed from the time-series prior to calculating the Allan variance."
Can you please give an expression (as explicitly as reasonably achievable here)
of this mentioned "(raw) output result before post-processing",
in terms of