  We discuss Transverse Momentum Dependent (TMD) gluon distributions within
high energy factorization at next-to-leading order in the strong coupling
within the framework of Lipatov's high energy effective action. We provide a
detailed discussion of both rapidity divergences related to the TMD definition
and its soft factor on the one hand, and rapidity divergences due to high
energy factorization on the other hand, and discuss common features and
differences between Collins-Soper (CS) and Balitsky-Fadin-Kuarev-Lipatov (BFKL)
evolution. While we confirm earlier results which state that the unpolarized
and linearly polarized gluon TMD agree in the BFKL limit at leading order, we
find that both distributions differ, once next-to-leading order corrections are
being included. Unlike previous results, our framework allows to recover the
complete anomalous dimension associated with Collins-Soper-Sterman (CSS)
evolution of the TMD distribution, including also single-logarithmic terms in
the CSS evolution. As an additional result we provide a definition of
$k_T$-factorization, i.e. matching of off-shell coefficients to collinear
factorization at next-to-leading order within high energy factorization and the
effective action framework. We furthermore establish a link between the QCD
operator definition of the TMD gluon distribution and a previously derived
off-shell TMD gluon-to-gluon splitting function, which is within the present
framework obtained as the real 1-loop correction.
