  Relativistic isobar ($^{96}_{44}$Ru+$^{96}_{44}$Ru and
$^{96}_{40}$Zr+$^{96}_{40}$Zr) collisions have revealed intricate differences
in their nuclear size and shape, inspiring unconventional studies of nuclear
structure using relativistic heavy ion collisions. In this study, we
investigate the relative differences in the mean multiplicity ($R_{\langle
N_{\rm ch}\rangle}$) and the second- ($R_{\epsilon_{2}}$) and third-order
eccentricity ($R_{\epsilon_{3}}$) between isobar collisions using initial state
models. It is found that initial fluctuations and nuclear deformations have
negligible effects on $R_{\langle N_{\rm ch}\rangle}$ in most central
collisions, while both are important for the $R_{\epsilon_{2}}$ and
$R_{\epsilon_{3}}$, the degree of which is sensitive to the underlying
nucleonic or sub-nucleonic degree of freedom. These features, compared to real
data, may probe the particle production mechanism and the physics underlying
nuclear structure.
