Self-supervised speech models can be trained to efficiently recognize spoken words in naturalistic, noisy environments. However, we do not understand the types of linguistic representations these models use to accomplish this task. To address this question, we study how S3M variants optimized for word recognition represent phonological and morphological phenomena in frequent English noun and verb inflections. We find that their representations exhibit a global linear geometry which can be used to link English nouns and verbs to their regular inflected forms. This geometric structure does not directly track phonological or morphological units. Instead, it tracks the regular distributional relationships linking many word pairs in the English lexicon -- often, but not always, due to morphological inflection. These findings point to candidate representational strategies that may support human spoken word recognition, challenging the presumed necessity of distinct linguistic representations of phonology and morphology.