Before revision:  and the lower bound by Eden and Rosenbaum [APPROX 2018] for approximately counting cliques, our results suggest that in our query model, approximately counting cliques is ``equivalent to'' exactly uniformly sampling cliques, in the sense that the query and time complexities of exactly uniform sampling and randomized approximate counting are within a polylogarithmic factor of each other.
After revision:  and the lower bound by Eden and Rosenbaum [APPROX 2018] for approximately counting cliques, our results suggest that in our query model, approximately counting cliques is "equivalent to" exactly uniformly sampling cliques, in the sense that the query and time complexities of exactly uniform sampling and randomized approximate counting are within a polylogarithmic factor of each other.