We report local probe (mu SR) measurements on the recently discovered tetragonal FeS superconductor which has been predicted to be electronically very similar to superconducting FeSe. Most remarkably, we find that low-moment (10(-2)-10(-3) mu B) disordered magnetism with a transition temperature of T-N approximate to 20 K microscopically coexists with bulk superconductivity below T-c = 4.3(1) K. From transverse field mu SR we obtain an in-plane penetration depth lambda(ab)(0) = 223(2) nm for FeS. The temperature dependence of the corresponding superfluid density lambda(-2)(ab)(T) indicates a fully gapped superconducting state and is consistent with a two gap s-wave model. Additionally, we find that the superconducting T-c of FeS continuously decreases for hydrostatic pressures up to 2.2 GPa.