One illustrative method disclosed herein includes, among other things, forming channel semiconductor material for a nano-sheet device and a transistor device, forming a device gate insulation layer on both the nano-sheet device and on the transistor device, and forming first and second sacrificial gate structures for the nano-sheet device and the transistor device. In this example, the method also includes removing the sacrificial gate structures so as to define, respectively, first and second gate cavities, wherein the device gate insulation layer is exposed within each of the gate cavities, removing the device gate insulation layer for the transistor device from within the first gate cavity while leaving the device gate insulation layer in position within the second gate cavity, and forming first and second replacement gate structures in the first and second gate cavities, respectively.