I would generally assume that parameter tuning is the process of finding the combination of hyperparameters (e.g., population size, crossover and mutation operators and rates, etc.) that yield the best performance on your problem. When you're thinking about the way that performance varies with parameter choice, this is the "what". What is the best choice of parameters.
Sensitivity analysis is the "how" or "how much". If I change my crossover rate from 0.9 to 1.0, how significant is the change in performance of my algorithm. Is my performance more or less stable across a wide range of choices (good) or is it highly dependent on finding this one little peak in the parameter space and every other choice is much worse (bad).