We prove finite-time input-to-state stability estimates for discrete-time time-varying linear systems in closed loop with sample-data control laws. The upper bounds for the norms of the states in the estimates are suprema of the uncertainties over time intervals of constant finite lengths. We cover output feedback stabilization and input delays. We combine our results with a trajectory based approach, to prove novel global exponential input-to-state stability estimates for nonlinear systems with state delays. We illustrate our work using a dynamics containing an unknown nonlinearity and an unknown state delay.