terminology - Is internal symmetry the same as gauge symmetry?

This is more a terminology question. I have seen that some people differentiate between the two types of symmetry: internal symmetry and gauge symmetry (of a field theory).

Is there a difference (in both local and global case), and if there is what is it?

Edit: For example in the case of Dirac equation interacting with electromagnetic field (plus the gauge fixing term) which is invariant under the set of local transformations:

$$\begin{equation} \psi \rightarrow e^{i\theta(x)}\psi\\ A_{\mu}\rightarrow A_{\mu} + \partial_{\mu}\theta(x) \end{equation}$$

which is internal symmetry (if any) and which is gauge symmetry?