Highly challenging, but if possible, a very nice energy source, and we're finally out of the steam age!
Magnetically confined D-He3 or H-B fusion could, in principle, be viable, because there is no detour through collecting hot neutrons, but is harder to achieve.
You propose a distinction where there is no difference.
It's most realistic application would be for space travel.
(And of course, that is also similar to the plasmas in a H-bomb, so there is a weapons aspect, but it's not like that we don't already know that H-bombs work.)
To avoid a turbine, you need a fuel whose output is mainly fast-moving charged particles.
Or, you might leave a (carefully-shaped) hole in one side of your reactor, and call it a nuclear rocket.
Just don't point the exhaust at anything inhabited.
Closed loop is actually not all that different from using a reactor as a generator. But instead of using your cooling system to power a turbine via a head exchanger, you use it to heat a reaction mass such as H2.
Open loop is closer to what you describe. Instead of indirectly heating your reaction mass, you run it directly through the hot reactor. It's simpler and lighter but your exhaust is extremely radioactive. Your reaction mass essentially doubles as the cooling system. Another downside to this approach is you cant run the reactor without making thrust. So lights out if you are coasting I guess.