Using the gauge principle we can derive the QED lagrangian from the dirac lagrangian, $$ \mathcal{L}_{Dirac}=\bar{\Psi}(i\gamma^{\mu} \partial_{\mu}-m\hat{I})\Psi $$ $$ \mathcal{L}_{QED}=\bar{\Psi}(i\gamma^{\mu} \partial_{\mu}-g\gamma^{\mu}A_{\mu}-m\hat{I})\Psi-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}. $$
If we apply Noethers first theorem to the Dirac lagrangian we find that it is invariant under global $U(1)$ transformations, with associated Noether's current: $$ \psi \rightarrow e^{iq\theta}\psi $$ $$ J^{\mu}=q\bar{\psi}\gamma^{\mu}\psi $$ This can be taken as a statement of charge conservation. Is the statement of conservation of charge via $J^{\mu}$ referring to global charge conservation (since we consider global transformations) or local charge conservation? Further, since the Dirac lagrangian represents the charged fermion field does $q$ here represent the total charge of the field or that of an individual fermion?
