The origin of the optical surface second-harmonic response at neat air/liquid and liquid /liquid interfaces is still a matter of debate. To elucidate this question, we first set out the basic equations describing the problem, essentially introducing, in an effective surface susceptibility tensor, the two contributions arising from the response of the bulk : the discontinuity of the normal component of the fundamental electromagnetic field and the molecular correlation in the vicinity of the surface. Then we discuss the difference in the magnitude and the ratio of the components of the tensor for the two types of interface, raising the problem of the strength of the field discontinuity at the boundary and the molecular ordering disparities near the interface. From our results, we conclude that in the case of the neat liquid/liquid interfaces, the main source of non-linearity arises from the surface itself rather than from the adjacent bulk solution.