It has been shown that random sampling from a generalized Zipf’s law yields Heaps’ law—that is, type-token growth following a power law. We investigate how correlations in the token ordering process disrupt this scaling. Using a one-parameter model, we reproduce a range of limiting cases in the type-token plane showing that the growth pattern does not uniquely reflect the underlying distribution. We illustrate this with individual discovery trajectories from Deezer users: while randomized sequences can be well fitted by power laws, real discovery trajectories display more diverse patterns—including linear growth—revealing the impact of temporal correlations and limitations of the Zipf/Heaps framework for describing individual discovery.