I am working with a commutative finite-dimensional $\mathbb C$-algebra $B$ and I am supposed to consider and prove a theorem about the hom-functors $$\text{Hom}_B(-,B)\quad\text{and}\quad \text{Hom}_{\mathbb C}(-,\mathbb C),$$ both of which are defined for $B\text{-mod}\rightarrow B\text{-mod}^{op}$. Here $B$-mod denotes the category of $B$-modules.
Can someone explain the difference between the two? I don't quite understand what the subscripts $B$ and $\mathbb C$ signify here and how the second one is even a functor that maps to $B$-mod$^{op}$.
Thanks!