Experimental measurements of proton acceleration with high intensity and high-contrast short laser pulses have been carried out over an order of magnitude range in target thickness and laser pulse duration. The dependence of the maximum proton energy with these parameters is qualitatively supported by two-dimensional particle-in-cell simulations. They evidence that two regimes of proton acceleration can take place, depending on the ratio between the density gradient and the hot electron Debye length at the rear target surface. As this ratio can be affected by the target thickness, a complex interplay between pulse duration and target thickness is observed. Measurements and simulations support unexpected variations in the laser absorption and hot electron temperature with the pulse duration and laser intensity, for which density profile modification at the target front surface is the controlling parameter.