There are various ways to define factorization algebras: one can define a factorization algebra that lives over the open subsets of some fixed manifold; or, alternatively, one can define a factorization algebra on the site of all manifolds of a given dimension (possibly with a specified geometric structure). In particular, we are interested in comparing $G$-equivariant factorization algebras on a fixed model space $\mathbb{M}$ to factorzation algebras on the site of all manifolds equipped with a $(\mathbb{M},G)$-structure, given by an atlas with charts in $\mathbb{M}$ and transition maps given by elements of $G$. I will review the definitions of these two concepts and then sketch the proof that they are equivalent.