The construct of response control or response inhibition is one of the cornerstones of modern cognitive psychology, featuring prominently in theories of executive functioning and impulsive behaviour. However, repeated failures to observe correlations between commonly applied tasks have led some theorists to question whether common or overlapping response conflict processes even exist. A challenge to answering this question is that behaviour is multifaceted, with both conflict and non-conflict processes (e.g. strategy, processing speed) contributing to individual differences. Here, we use a cognitive model to dissociate these processes; the diffusion model for conflict tasks (Ulrich et al., 2015). In a meta-analysis of fits to 7 empirical datasets, we observed weak (rho<.05) correlations between tasks in parameters reflecting conflict processing, seemingly challenging a general control construct. However, we saw consistent positive correlations in parameters representing processing speed and strategy. We then use model simulations to evaluate whether correlations in behavioural costs are diagnostic of the presence or absence of common mechanisms of conflict processing. We compare correlations in simulated behaviour in scenarios where we impose correlations in conflict parameters to scenarios in which only non-conflict parameters are correlated. We find that correlations in behaviour are neither necessary nor sufficient evidence for correlations in conflict parameters. Our data provide converging evidence to claims that non-conflict processes contribute substantially to individual differences in conflict tasks and illustrate that correlations between conflict tasks are only weakly informative about common conflict mechanisms.