  The continuously expanding sample of gravitational-wave observations is
revealing the formation and evolutionary mechanism of merging compact binaries.
Two primary channels, namely, isolated field binary evolution and dynamical
capture, are widely accepted as potential producers of merging binary black
holes (BBHs), which are distinguishable with the spin-orientation distributions
of the BBHs. We investigate the two formation channels in GWTC-3, with a
dedicated semi-parametric population model, i.e., a mixture of two
sub-populations with different spin-orientation distributions (one is
nearly-aligned and the other is nearly-isotropic). It turns out that the two
sub-populations have different mass and mass-ratio distributions. The
nearly-aligned sub-population, which is consistent with the isolated field
formation channels, has a less preference for symmetric systems, and likely
dominate the 10-solar-mass peak in the primary-mass function. While the
isotropic sub-population shows a stronger preference for symmetric systems, and
mainly contribute to the 35-solar-mass peak in the primary-mass function,
consistent with the dynamical channels. Moreover, our results show that the
purely isotropic-spin and the single well-aligned (i.e., the width of
$\cos\theta$ distribution $\sigma_{\rm t}<0.5$) scenario are ruled out (by a
Bayes factor of $\ln\mathcal{B}=5.2$ and $\ln\mathcal{B}=9.8$).
