Strong or weak force between protons and neutrons?
I think it is a poor phrasing. The strong force is responsible for keeping quarks together inside a proton or a neutron, but also between quarks belonging to different proton/neutron (but I am not sure for proton-proton interaction because of the repulsive electromagnetic force).

By contrast, the weak force is responsible for turning one type of quarks into another type or quarks, thus transforming a proton into a neutron in the case of beta+ radioactive decay, with emission of a positron (the overall charge is always conserved).