I have an embarrassingly basic confusion about the definition of Drinfeld modules. I think that the definition of a Drinfeld module over $S$ should be "a $\mathbb{G}_a$-torsor over $S$ and ...".
However it is quite common to find in the literature a definition that begins "A Drinfeld module over $S$ is a line bundle over $S$ and ... ". This seems very misleading to me, as what is usually called a line bundle corresponds to a $\mathbb{G}_m$-torsor, not a $\mathbb{G}_a$-torsor. Of course these look locally the same if one is only paying attention to the underlying scheme, but they should be very different notions.
Am I missing something here? It seems much more likely that I'm confused than large swaths of the internet, but I'm not seeing why the definition of Drinfeld module would be the same if you use $\mathbb{G}_a$-torsors or $\mathbb{G}_m$-torsors.
