Interspecific interactions, including host-symbiont associations, can profoundly affect the evolution of the interacting species. Given the phylogenies of host and symbiont clades and knowledge of which host species interact with which symbiont, two questions are often asked: “Do closely related hosts interact with closely related symbionts?” and “Do host and symbiont phylogenies mirror one another?”. These questions are intertwined and can even collapse under specific situations, such that they are often confused one with the other. However, in most situations, a positive answer to the first question, hereafter referred to as “cophylogenetic signal”, does not imply a close match between the host and symbiont phylogenies. It suggests only that past evolutionary history has contributed to shaping present-day interactions, which can arise, for example, through present-day trait matching, or from a single ancient vicariance event that increases the probability that closely related species overlap geographically. A positive answer to the second, referred to as “phylogenetic congruence”, is more restrictive as it suggests a close match between the two phylogenies, which may happen, for example, if symbiont diversification tracks host diversification or if the diversifications of the two clades were subject to the same succession of vicariance events. Here we apply a set of methods (ParaFit, PACo, and eMPRess), which significance is often interpreted as evidence for phylogenetic congruence, to simulations under three biologically realistic scenarios of trait matching, a single ancient vicariance event, and phylogenetic tracking with frequent cospeciation events. The latter is the only scenario that generates phylogenetic congruence, whereas the first two generate a cophylogenetic signal in the absence of phylogenetic congruence. We find that tests of global-fit methods (ParaFit and PACo) are significant under the three scenarios, whereas tests of event-based methods (eMPRess) are only significant under the scenario of phylogenetic tracking. Therefore, significant results from global-fit methods should be interpreted in terms of cophylogenetic signal and not phylogenetic congruence; such significant results can arise under scenarios when hosts and symbionts had independent evolutionary histories. Conversely, significant results from event-based methods suggest a strong form of dependency between hosts and symbionts evolutionary histories. Clarifying the patterns detected by different cophylogenetic methods is key to understanding how interspecific interactions shape and are shaped by evolution.