I read this and other similar questions, but they all address the problem of gauging a global symmetry (implying that one could also gauge a local one).
This confused me a lot: in my mind gauge and local are synonyms when used for symmetries, and "gauging" meant something like "localizing". Is this wrong? What are the proper definitions of gauge symmetry and of the process of gauging a symmetry?
Edit: this answer seems to prove my point, saying that a gauge symmetry is a local symmetry after you add the gauge bosons to make the lagrangian usable. If this is correct, then what is the meaning of "gauging"?
Edit 2: this paper uses the wording
Therefore when one wishes to solve the equations of motion describing the gauge field, the local gauge invariance of the Lagrangian, and so the action, is destroyed along with the possibility of additional observables. On the other hand, global gauge invariance still holds and one is left with the corresponding intrinsic conserved current and charge.
Which seems to be against what @CosmasZachos said in the comments. What does global gauge mean?