Statistical learning—extracting the underlying structure of complex environments from ongoing exposure to sensory inputs—is a key mechanism by which humans and other animals acquire generalizable internal representations of the world (i.e., a form of semantic memory). While the kinds of statistical structures that are extracted from stimuli over the course of statistical learning, and the way they generalize to novel test stimuli, have been characterized in great detail, the resulting internal representations have typically been assessed by two-alternative forced-choice tests that simply measure generic familiarity (i.e., memory strength). Hence, it remains unknown how the learning of statistical structure is related to learning, storing, and recalling memories with fine detail and context. Conversely, recognition-memory research has characterized the specificity and context-dependence of memories by using test methods that analyze hit and false-alarm rates of memory judgements through Receiver Operating Characteristic (ROC) curves. Based on these studies, the dual-process theory posits that recognition memory relies on two distinct processes: familiarity and recollection (retrieval of contextual details). However, recognition memory has typically been studied using stimuli that had strong pre-existing semantic representations (e.g., words, natural scenes), and in particular test stimuli that were either exactly repeated from training or entirely novel. Thus, it remains unknown how memories of non-semantic stimuli are recalled and in particular how familiarity and recollection contribute to memory-based generalization. As a first step toward unifying these fields, we investigated whether the dual-process theory generalizes to memory representations emerging through visual statistical learning. Across six online experiments (each with N = 50), participants completed recognition tasks after exposure-based learning requiring different degrees of generalization between familiarization and test. In Experiment 1, participants were familiarized with pairs of simple visual shapes and tested on either the same pairs (targets) or recombined pairs (lures). In Experiment 2, we replaced the shapes in the lures with entirely novel shapes. In Experiment 3, we tested individual familiar shapes against novel shapes, while in Experiment 4, we reversed the structure of Experiment 3 by familiarizing participants with single shapes and testing them on pairs. Experiment 5 involved single-shape familiarization and testing, and Experiment 6 repeated Experiment 1 but with increased. Across these experiments, we found that recollection probability was highest when participants were tested on single items. Conversely, familiarity was stronger when fewer items were presented during familiarization and when novelty contrast was higher at test (e.g., Experiments 2 vs. 1). Prior recognition-memory studies suggest that item recognition should engage both recollection and familiarity, while associative recognition (distinguishing true vs. recombined pairs) should rely primarily on recollection. Our results support the joint contribution of recollection and familiarity in experiments with tests based on items. However, in contrast with previous findings, we find that recognition in non-semantic contexts is predominantly driven by familiarity. In addition to this indication of differences in how semantic and non-semantic stimuli engage familiarity and recollection, the present study highlights the paramount influence of contextual factors, such as familiarization–test relations, on recognition performance.