global vs gauge symmetry
Imagine a vast army where everyone must turn at once. A global command is 'everybody turn 90 degrees right' — one instruction, the same for the whole army, executed in lockstep. A local command would be different: each soldier gets to choose their own turn, independently, person by person. This distinction — one change applied everywhere identically, versus a change you can make differently at every point — is the heart of the difference between a global symmetry and a gauge (local) symmetry.
A global symmetry is a transformation you apply the same way everywhere in space and time at once. The conservation laws from Noether's theorem — energy, charge, baryon number — come from global symmetries. A gauge symmetry (also called a local symmetry) is far more demanding: it insists the laws stay unchanged even if you make the transformation differently at every separate point in space and time. That is a much stronger requirement, and nature can only satisfy it by introducing force-carrying particles whose whole job is to compensate for the point-by-point differences. Remarkably, demanding this local symmetry for electric charge forces the photon into existence; demanding it for color charge forces the gluons; demanding it for the weak charges forces the W and Z bosons.
This is one of the deepest ideas in the Standard Model: the fundamental forces are not bolted on by hand but are the inevitable consequence of insisting on gauge symmetries. A merely global symmetry gives you a conservation law; a gauge symmetry gives you a whole force. The distinction also matters because global symmetries can be broken or be approximate (like isospin) without disaster, whereas an exact gauge symmetry is tightly constrained — it is what keeps the photon massless, for instance. The mechanics of how gauge symmetry builds forces belong to the gauge-theory and quantum-field-theory entries; here the point is simply the global-versus-local contrast.
Electric-charge conservation comes from a global symmetry of the electromagnetic field. Promote that same symmetry to a local one — demand it hold independently at every point in spacetime — and you are forced to introduce a new field, whose particle is the photon. The global version conserves charge; the local version creates electromagnetism itself.
A global symmetry conserves charge; making it local creates the photon.
Strictly, a gauge symmetry is not a symmetry that relates different physical states at all — it is a redundancy in how we describe one and the same state. That subtlety is why gauge 'symmetry' cannot be spontaneously broken in the naive sense, a point developed in the gauge-theory entries.