Although the low energy fractional excitations of one dimensional integrable
models are often well-understood, exploring quantum dynamics in these systems
remains challenging in the gapless regime, especially at intermediate and high
energies. Based on the algebraic Bethe ansatz formalism, we study spin dynamics
in the antiferromagnetic spin-$\frac{1}{2}$ XXZ chain with the Ising anisotropy
via the form-factor formulae. Various excitations at different energy scales
are identified crucial to the dynamic spin structure factors under the guidance
of sum rules. At small magnetic polarizations, gapless excitations dominate the
low energy spin dynamics arising from the magnetic-field-induced
incommensurability. In contrast, spin dynamics at intermediate and high
energies is characterized by the two- and three-string states, which are
multi-particle excitations based on the commensurate N\'eel ordered background.
Our work is helpful for experimental studies on spin dynamics in both condensed
matter and cold atom systems beyond the low energy effective Luttinger liquid
theory.