Nuclear fusion is relatively well understood and is now an engineering problem - we're past the "how does it work" part and into the "how can we practically apply this understanding.
We have been able to use fusion in thermonuclear devices for half a century. Also the Fusor, is a fusion reactor, just not a very efficient one, but one that is easily built. Again for nearly 50 years. We are well into how can we do this with efficiently so that it is commercially useful. While they aren't commercially used to produce energy, Fusors are sold as a neutron source and have been used for transmutation of elements. ITER want commercially viable fusion.
Cold fusion is not on the same footing.
Cold fusion is like filling your regular car up with water and saying its going to do 10,000 km on a tank. There are deep and serious reasons why this can't happen and why its all wrong. No one is measuring neutrons, with no neutrons its not fusion. The energy output looks a lot more like a chemical reaction. (AFAIK - I haven't been looking at any "new" stuff because its so dodgy).
We can sustain Fusion for 6 min 30 in a tokamak. There is progress being made on fusion. ITER has high hopes. Interestingly various green parties/antinuclear groups and movements oppose the the ITER.
The US Navy invested quite a bit into something called a Polywell. However, they haven't exactly been pouring money into it. They see it more as a curious project than a viable source of energy. However its a very curious design, and has had surprisingly promising results. Yet no one knows about the research in Polywells but everyone knows about Cold Fusion.