  We put forward the exact version of two-parameter generating functions with
$\tau$-invariance, which allows us to give a unified and inherent definition
for the Drinfeld realization of two-parameter quantum affine algebras for all
the untwisted types. As verification, we first construct their level-one vertex
representations of $U_{r,s}(\widehat{\mathfrak{g}})$ for simply-laced types,
which in turn well-detect the effectiveness of our definitions both for
$(r,s)$-generating functions and $(r,s)$-Drinfeld realization in the framework
of establishing the two-parameter vertex representation theory.
