Many samplers are based on HMC, it's a general class of samplers, not a specific algorithm. NUTS is a variation of HMC, as well as the paper I linked above.
'vanilla' HMC uses detailed balance to guarantee that the stationary distribution of the chain is the one you want, causing the process to behave like a random walk. So although the Hamiltonian bit of HMC lets you take these great big steps through state space, you end up retracing your steps quite a lot.
'vanilla' HMC uses detailed balance to guarantee that the stationary distribution of the chain is the one you want, causing the process to behave like a random walk. So although the Hamiltonian bit of HMC lets you take these great big steps through state space, you end up retracing your steps quite a lot.
Hence NUTS (No-U-turn sampler) et. al