  We theoretically study the dynamics of a transverse-field Ising chain with
power-law decaying interactions characterized by an exponent $\alpha$, which
can be experimentally realized in ion traps. We focus on two classes of
emergent dynamical critical phenomena following a quantum quench from a
ferromagnetic initial state: The first one manifests in the time averaged order
parameter, which vanishes at a critical transverse field. We argue that such a
transition occurs only for long-range interactions $\alpha \leq 2$ . The second
class corresponds to the emergence of time-periodic singularities in the return
probability to the ground state manifold (a.k.a. Loschmidt echo) which is
obtained for all values of $\alpha$ and agrees with the order parameter
transition for $\alpha\leq 2$. We characterize how the two classes of
nonequilibrium criticality correspond to each other and give a physical
interpretation based on the symmetry of the time-evolved quantum states.
