Nuclear reactor’s create heat - for transportation it’s all a matter of converting that heat energy into some form of thrust.
In an airplane a “combustion engine” (which uses heat created by the burning of a fuel) drives a turbine. Nuclear powered naval craft use the heat’s reactor to turn water into steam to drive a turbine and the turbine driving “the screw”.
But, it’s all a matter of what you do with the energy from the reactor.
A nuclear powered space vehicle might use a “nuclear electric system”, where nuclear reactors are a heat source for electric ion drives, to expel plasma out of nozzles to propel & maneuver spacecraft already in space.
Apparently NASA thinks so too and has R&D programs in the hopper, with Boeing and others, to investigate the idea.
Both of your first examples require some form of medium to travel in. Space doesn’t have enough friction in order to obtain any kind of useful propulsion.
And yes, ion drives have potential, but they haven’t been developed yet to a point where they might be used on a test flight to the moon/mars, much less as a reliable means of propulsion.