A key question in many network studies is whether the observed correlations between units are primarily due to contagion or latent confounding. Here, we study this question using a segregated graph (Shpitser, 2015) representation of these mechanisms, and examine how uncertainty about the true underlying mechanism impacts downstream computation of network causal effects, particularly under full interference -- settings where we only have a single realization of a network and each unit may depend on any other unit in the network. Under certain assumptions about asymptotic growth of the network, we derive likelihood ratio tests that can be used to identify whether different sets of variables -- confounders, treatments, and outcomes -- across units exhibit dependence due to contagion or latent confounding. We then propose network causal effect estimation strategies that provide unbiased and consistent estimates if the dependence mechanisms are either known or correctly inferred using our proposed tests. Together, the proposed methods allow network effect estimation in a wider range of full interference scenarios that have not been considered in prior work. We evaluate the effectiveness of our methods with synthetic data and the validity of our assumptions using real-world networks.