An electromagnetic duality is a duality that maps electric to magnetic degrees of freedom of two distinct theories. Apart from source-less Maxwell electrodynamics, other theories require magnetic monopoles. I am not an expert in ($N=1$) Seiberg duality but as far as I know there is no magnetic charges in it. So why is it called an electromagnetic duality? Where are the "magnetic" degree of freedom of the theories? My guess is just because it is also an S-duality such as the Montonen-Olive or GNO dualities. Yet their are much different. The EM duality in the sense of Montonen-Olive is exact in the sense that it is (conjectured) valid at any scale. The Seiberg duality however is a map valid only at particular regimes. The Seiberg duality maps the IR regime of the "electric" theory to an IR free regime of a "magnetic" theory. This map is not valid along the RG flow.
Note: I now that Seiberg assume magnetic monopoles in the theory. But how do these monopoles appear? If they are topological solutions, where is the spontaneous symmetry breaking pattern? Where is the homotopy condition for stable monopoles? Where are the field confiturations of these solitons? Where is the magnetic charge quantization? What are the topological charge or topological sectors of these monopoles?