Despite progress in drug development, a quantitative and physiological understanding of how small-molecule inhibitors act on cells is lacking. Here, we measure the signalling and proliferative response of individual primary T-lymphocytes to a combination of antigen, cytokine and drug. We uncover two distinct modes of signalling inhibition: digital inhibition (the activated fraction of cells diminishes upon drug treatment, but active cells appear unperturbed), versus analogue inhibition (the activated fraction is unperturbed whereas activation response is diminished). We introduce a computational model of the signalling cascade that accounts for such inhibition dichotomy, and test the model predictions for the phenotypic variability of cellular responses. Finally, we demonstrate that the digital/analogue dichotomy of cellular response as revealed on short (signal transduction) timescales, translates into similar dichotomy on longer (proliferation) timescales. Our single-cell analysis of drug action illustrates the strength of quantitative approaches to translate in vitro pharmacology into functionally relevant cellular settings.