FAD is the FeynCalc external form of FeynAmpDenominator and denotes an inverse propagator.
FAD[q, q-p, ...] is \frac{1}{q^2 (q-p)^2 \ldots}.
FAD[{q1,m}, {q1-p,m}, q2, ...] is \frac{1}{[q1^2 - m^2][(q1-p)^2 - m^2] q2^2}. Translation into FeynCalc internal form is performed by FeynCalcInternal.
Overview, FAD, FCE, FCI, FeynAmpDenominator, FeynAmpDenominatorSimplify, PropagatorDenominator.
FAD[q, p - q]\frac{1}{q^2.(p-q)^2}
FAD[p, {p - q, m}]\frac{1}{p^2.\left((p-q)^2-m^2\right)}
FAD[{p, 0, 2}, {p - q, m, 3}]\frac{1}{\left(p^2\right)^2.\left((p-q)^2-m^2\right)^3}
FAD[q, p - q] // FCI // StandardForm
(*FeynAmpDenominator[PropagatorDenominator[Momentum[q, D], 0], PropagatorDenominator[Momentum[p, D] - Momentum[q, D], 0]]*)FAD[p] FAD[p - q] // FeynAmpDenominatorCombine[#, FCE -> True] & // StandardForm
(*FAD[p, p - q]*)