The harmonic approximation gives a non-zero kinetic energy at 0 K for which Heisenberg's uncertainty principle is used as an explanation. A particle at 0 K couldn't be stationary because that would violate its wave-like nature.
Then there is the talk of zero-point potential energy. By the virtue of its existence, a particle with a finite mass would hold some energy within itself irrespective of being or not being in motion.
The first is easy to understand. The second, though, it would make sense only if the particle was in some field that exerts potential on it. Are there implications here that come from theories that a casually thermodynamics-educated person wouldn't comprehend?
Also, am I right to assume that the term zero-point energy, when used in atomistic modeling literature, is used solely to mean the first kind described above?