Why do we use the word 'current' when discussing the weak force?

So, for example, my notes go through fermi theory, in which case the interactions are:
$$
G_F j^dagger_mu j^mu
$$
where
$$
j_mu = barνγ_µe + bar pγ_µn +…
$$

why is $j_mu$ called a current here? Is it related to a noether current in some way?