NO.

In some cities/countries there is however another city-rail-system, f.e. often in Germany, there it is called S-bahn. In FRAnkfurt (and München and Stuttgart) it even runs in a tunnel under the centre. THESe trains-labelled as DB (=deutsche bahn) you can use, BUT you also have to use travelday and write the used sector. Same for SBB in Zúri. Hence for just short rides it makes no sense. About any larger city in EUR has some kind of day or 24-hr pass for all transit-often also like citycard, including entrance to musea and attractions or discounts. These passes for only transit usually cost like 6-8€/day.

funfact: Zurich has no Metro, but two lines use a station that was built to become main stations metro station!

But this lines  (S4 and S10) are not included into your pass!