The freedom we have in choosing the vector potential $\vec{A}$ in E&M is referred to as the gauge freedom, whereas in general relativity (GR), we refer to the freedom to choose any coordinate system as the gauge freedom.

We do have such freedom of choosing coordinate systems (related by a Lorentz boost) in E&M. Why then this freedom is not called the gauge freedom (taking inspiration from GR)? In fact, this freedom is not given any special name/mention. Or is it?