One illustrative integrated circuit product disclosed herein includes, among other things, a plurality of FinFET devices, each of which comprises a gate structure comprising a high-k gate insulation material and at least one layer of metal, a single diffusion break (SDB) isolation structure positioned in a first trench defined in a semiconductor substrate between first and second active regions, the SDB isolation structure comprising the high-k insulating material and the at least one layer of metal, and a double diffusion break (DDB) isolation structure positioned in a second trench defined in a semiconductor substrate between third and fourth active regions, the DDB isolation structure comprising a first insulating material that substantially fills the second trench.