Humans have a remarkable capacity for perceiving and producing rhythm. Rhythmic competence is often viewed as a single concept, with participants who perform more or less accurately on a single rhythm task. However, research is revealing numerous sub-processes and competencies involved in rhythm perception and production, which can be selectively impaired or enhanced. To investigate whether different patterns of performance emerge across tasks and individuals, we measured performance across a range of rhythm tasks from different test batteries. Distinct performance patterns could potentially reveal separable rhythmic competencies that may draw on distinct neural mechanisms. Participants completed nine rhythm perception and production tasks selected from the Battery for the Assessment of Auditory Sensorimotor and Timing Abilities (BAASTA), the Beat Alignment Test (BAT), the Beat-Based Advantage task (BBA), and two tasks from the Burgundy best Musical Aptitude Test (BbMAT). Principal component analyses revealed clear separation of task performance along three main dimensions: production, beat-based rhythm perception, and sequence memory-based rhythm perception. Hierarchical cluster analyses supported these results, revealing clusters of participants who performed selectively more or less accurately along different dimensions. The current results support the hypothesis of divergence of rhythmic skills. Based on these results, we provide guidelines towards a comprehensive testing of rhythm abilities, including at least three short tasks measuring: (1) rhythm production (e.g., tapping to metronome/music), (2) beat-based rhythm perception (e.g., BAT), and (3) sequence memory-based rhythm processing (e.g., BBA). Implications for underlying neural mechanisms, future research, and potential directions for rehabilitation and training programs are discussed.