Why do currents, functionals on compactly supported differentiable n-forms, bare the name they do?

I've assumed that it has something to do with an electrical current being formalized as a vector field along a curve or other submanifold, but this is nothing but a guess.

Why do currents, functionals on compactly supported differentiable n-forms, bear the name they do?

I've assumed that it has something to do with an electrical current being formalized as a vector field along a curve or other submanifold, but this is nothing but a guess.