We revisit the expressions for pressure in atomic and molecular coordinates. We elaborate on the proof of their equivalence, reported previously by one of us (Comp. Phys. Rep. 1986, 4, 345-392), by taking into account the boundary conditions appropriate to the system of interest. For systems subject to closed boundaries, we obtain the difference between atomic and molecular pressure, which is shown to vanish in the thermodynamic limit. For systems subject to periodic boundaries, we derive expressions for atomic and molecular pressure and proof their equivalence.