Difference between S and I in the context of magnetic resonance experiments In the lecture our professor told us that nuclei with $S&gt;1/2$ have a quadrupole and are therefore detected with NQR instead of NMR.
The majority of all elements have nuclei with $S&gt;1/2$.

I wondered why he used $S$ (electron spin) instead of $I$ (nuclear spin) in the slides?
The nomenclature you mean has nothing to do with the electron spin S, it is something completely different. In heteronuclear experiments with two spins it is common to call them $I$ and $S$, with $I$ being the more sensitive nucleus. They're still both spin 1/2 nuclei.

$I$ is one spin, and $S$ is a different spin in this nomenclature, with a scalar coupling between them.

This nomenclature is usually introduced with the INEPT transfer and experiments like HSQC or HMQC.