  The equivariant bordism classification of manifolds with group actions is an
essential subject in the study of transformation groups. We are interesting in
the action of 2-torus group $\mathbb{Z}_2^n$ and torus group $T^n$, and study
the equivariant bordism of 2-torus manifolds and unitary toric manifolds. In
this paper, we give a new description of the group
$\mathcal{Z}_n(\mathbb{Z}_2^n)$ of 2-torus manifolds, and determine the
dimention of $\mathcal{Z}_n(\mathbb{Z}_2^n)$ as a $\mathbb{Z}_2$-vector space.
With the help of toric topology, L\"u and Tan proved that the bordism groups
$\mathcal{Z}_n(\mathbb{Z}_2^n)$ are generated by small covers. We will give a
new proof to this result. These results can be generalized to the equivariant
bordism of unitary toric manifolds, that is, we will give a new description of
the group $\mathcal{Z}_n^U(T^n)$ of unitary torus manifolds, and prove that
$\mathcal{Z}_n^U(T^n)$ can be generated by quasitoric manifolds with
omniorientations.
