Adaptive sampling allows adding sample units in the vicinity of a sample unit selected in the original design, generally used in situations in which the response of interest is clustered or aggregated. (After Lohr, p. 403).
Auxiliary variables are "extra" variables measured in association with the desired response variable that might be used to increase precision of the estimate, by for example developing a modeled relationship between the response variable and auxiliary variables that might be measured at more sites than can be monitored for the primary response variable. Auxiliary variables are used in model assisted surveys to guide the selection of the sample sites. (loosely from Lohr, p. 60-61).
Adaptive sampling
