Background: Maximal handgrip strength (HGS) could be an incomplete and unidimensional measure of muscle function. This pilot study sought to examine the relationships between maximal HGS, radial and ulnar digit grip strength, submaximal HGS force control, HGS fatigability, neuromuscular HGS steadiness, and HGS asymmetry in older adults. Methods: A digital handgrip dynamometer and accelerometer was used to collect several HGS measurements from 13 adults aged 70.9 ± 4.0 years: maximal strength, radial and ulnar digit grip strength, submaximal force control, fatigability, neuromuscular steadiness, and asymmetry. Pearson correlations determined the relationships between individual HGS measurements. A principal component analysis was used to derive a collection of new uncorrelated variables from the HGS measures we examined. Results: The individual HGS measurements were differentially correlated. Maximal strength (maximal HGS, radial digit strength, ulnar digits strength), contractile steadiness (maximal HGS steadiness, ulnar digit grip strength steadiness), and functional strength (submaximal HGS force control, HGS fatigability, HGS asymmetry, HGS fatigability steadiness) emerged as dimensions from the HGS measurements that we evaluated. Conclusion: Our findings suggest that these additional measures of muscle function may differ from maximal HGS alone. Continued research is warranted for improving how we assess muscle function with more modern technologies, including handgrip dynamometry and accelerometry.