  Transverse-momentum-dependent (TMD) gluon distributions have different
operator definitions, depending on the process under consideration. We study
that aspect of TMD factorization in the small-x limit, for the various
unpolarized TMD gluon distributions encountered in the literature. To do this,
we consider di-jet production in hadronic collisions, since this process allows
to be exhaustive with respect to the possible operator definitions, and is
suitable to be investigated at small x. Indeed, for forward and nearly
back-to-back jets, one can apply both the TMD factorization and Color Glass
Condensate (CGC) approaches to compute the di-jet cross-section, and compare
the results. Doing so, we show that both descriptions coincide, and we show how
to express the various TMD gluon distributions in terms of CGC correlators of
Wilson lines, while keeping Nc finite. We then proceed to evaluate them by
solving the JIMWLK equation numerically. We obtain that at large transverse
momentum, the process dependence essentially disappears, while at small
transverse momentum, non-linear saturation effects impact the various TMD gluon
distributions in very different ways. We notice the presence of a geometric
scaling regime for all the TMD gluon distributions studied: the "dipole" one,
the Weizs\"acker-Williams one, and the six others involved in forward di-jet
production.
