As first recognized by Hill in 1960's, one character distinguishing the thermodynamics of small systems from the macroscopic one is that some intensive variables are no longer defined uniquely for small systems. For example, the differential chemical potential, defined as the derivative of a thermodynamic potential with respect to particle number, is no longer equal to the integral one, given by the ratio of Gibbs free energy to the particle number. The concept of differential and integral surface tensions has been introduced recently to account for the increasing surface contribution to thermodynamic potentials when a system shrinks down in size. Simulations constitute a powerful tool for testing new concepts. The present work provides the simulation evidence for distinct differential and integral surface tensions. Our results point out some useful directions for future experimental investigations to check the general validity of the concept of differential and integral surface tensions.