In this paper, we study the properties of toric $\sigma$-varieties and toric $p[\sigma]$-varieties. Toric $\sigma$-varieties and toric $p[\sigma]$-varieties are generalizations of toric varieties in difference case. Every affine toric variety corresponds an affine semigroup. Similarly, every toric $\sigma$-variety corresponds to an affine $\mathbb{N}[x]$-semimodule and every affine toric $p[\sigma]$-variety corresponds to an affine $p[x]$-semimodule. It turns out many properties of toric varieties can be generalized to toric $\sigma$-varieties and toric $p[\sigma]$-varieties, such as the orbit-face correspondence and the divisor theory.