They're not different at all! Seiberg has used the term electric-magnetic duality in the title of his famous paper, too.

His duality is an electric-magnetic duality because the duality relates two descriptions and objects that are electrically charged under the gauge group on one side (e.g. quarks and gluons) are mapped to solitons (forms of magnetic monopoles) carrying the magnetic monopole charges under the gauge group in the dual description! So just like there is an "$SU(3)$-like" electric field $F_{0i}$ around a quark or gluon in the electric description, the same object looks like a magnetic field $F_{jk}$ in the dual description – and under the other description's gauge group.

Because this duality avoids an immediate contradiction, it must simultaneously be an S-duality, too. It couldn't be a weak-weak duality because the weak-coupling physics of any gauge theory is basically unique. "Easy to construct" excitations (quarks and gluons) may only be mapped to "complicated objects" (solitons) if the coupling is strong on one side.

Seiberg duality *is* just a generalization of the usual $F_{\mu\nu}\to *F_{\mu\nu}$ electric-magnetic duality of the Maxwell's theory, a generalization with different and more complex gauge groups on both sides, supersymmetry, and some quark matter. In Maxwell's theory, one can arguably "ban" magnetic monopoles but in non-Abelian gauge theories with complicated enough spectrum, they're basically unavoidable because one may construct them as classical solitonic solutions and these objects have to exist in the quantum theory, too.

In $d=4$, electric-magnetic duality and S-duality are basically synonyms. In different spacetime dimensionalities, these two notions become different because the electric-magnetic duality exchanges point-like charges with some branes of a different dimension while an S-duality should preserve the dimensionality (and location) of objects. To allow a more general symmetry that mixes the charges of different dimensions etc., one has to call it a U-duality.

This post imported from StackExchange Physics at 2016-07-13 17:19 (UTC), posted by SE-user Luboš Motl