  We give an explicit correspondance between Costantino$-$L\^e's stated skein
algebras, which are defined via explicit relations on stated tangles, and
Gunningham$-$Jordan$-$Safronov's internal skein algebras, a.k.a
Ben-Zvi$-$Brochier$-$Jordan's moduli algebras, which are defined as internal
endomorphism algebras. For the sake of accessibility, we do not use
factorisation homology but compute it using Cooke's skein categories. Stated
skein algebras are defined on surfaces with multiple boundary edges and we
generalise internal skein algebras in this context. We prove excision
properties of multi-edges internal skein algebras using excision properties of
skein categories, and agreeing with excision properties of stated skein
algebras when $\mathcal{V} = \mathcal{U}_{q^2}(SL_2)\text{--}mod^{fin}$.
