We present distinct, a general method for differential analysis of full distributions that is well suited to applications on single-cell data, such as single-cell RNA sequencing and high-dimensional flow or mass cytometry data. High-throughput single-cell data reveal an unprecedented view of cell identity and allow complex variations between conditions to be discovered; nonetheless, most methods for differential expression target differences in the mean and struggle to identify changes where the mean is only marginally affected. distinct is based on a hierarchical nonparametric permutation approach and, by comparing empirical cumulative distribution functions, identifies both differential patterns involving changes in the mean as well as more subtle variations that do not involve the mean. We performed extensive benchmarks across both simulated and experimental datasets from single-cell RNA sequencing and mass cytometry data, where distinct shows favourable performance, identifies more differential patterns than competitors, and displays good control of false positive and false discovery rates. distinct is available as a Bioconductor R package.