s-parametrized quantization is essential to phase space theory of quantum mechanical. Based on s-ordered Wigner operator, we examine the classical correspondence of the s2-parametrized Wigner operator through the s1-parametrized quantization scheme, and establish the mutual transformation relation between different s-parametrized quantization schemes. It turns out that the s-parametrized Wigner operator's s-ordering is just the Dirac delta function, which seems to be a new result. As applications, we derive the s-ordered form of the density operator of thermal states and some new generating function formula of Hermite polynomials.