In this research article, we have studied the results of P. Sahoo and H. Karmakar, intending to determine, in any manner, whether it is possible to relax the nature of sharing by replacing the shift of non-constant transcendental entire functions of nite order with the product of shift. In this direction, we have investigated the uniqueness of shift dierence polynomials of two entire functions when they share a non-zero polynomial with a nite weight and one being the Mobius transformation of the other satisfying n  2d + 3, and also when they share a small function with a nite weight satisfying n  m +  + 5: We also investigate the same situation when the original functions f and g share the value zero counting multiplicities (CM) satisfying n > 2(􀀀1 + d) : Our results in this paper extend and generalizes the previous results of P. Sahoo and H. Karmakar [Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2017, 52 (2), pp.102-110].