For a half century, the calculation of local pressure components and surface tension along the normal to the surface have been carried out using mechanical definitions. This has led to three principal definitions: Irving and Kirkwood, Harasima and Kirkwood-Buff. Recently, thermodynamic definitions based on the energy calculation have been introduced to compute the local properties. We propose here to compare both definitions for Lennard-Jones particles interacting through a truncated and shifted potential. For this, two locations of the pairwise interaction involved in the calculation of the local pressure components and surface tension within the thermodynamic routes are investigated. For the first time, we show that the thermodynamic definition suffers, to one least degree with respect to the mechanical definition, from the same ambiguity. From a numerical standpoint, thermodynamic definition is more simple and less computationally expensive. Therefore, with the complicated potential, the thermodynamic approach appears to be most interesting to compute macroscopic and local pressure and surface tension.