  Rashba spin splitting in two-dimensional (2D) semiconductor systems is
generally calculated in a ${\bf k} \cdot {\bf p}$ Luttinger-Kohn approach where
the spin splitting due to asymmetry emerges naturally from the bulk band
structure. In recent years, several new classes of 2D systems have been
discovered where electronic correlations are believed to have an important
role. In these correlated systems, the effects of asymmetry leading to Rashba
splitting have typically been treated phenomenologically. We compare these two
approaches for the case of 2D electron systems in SrTiO$_3$-based
heterostructures, and find that the two models produce fundamentally different
behavior in regions of the Brillouin zone that are particularly relevant for
magnetotransport. Our results demonstrate the importance of identifying the
correct approach in the quantitative interpretation of experimental data, and
are likely to be relevant to a range of 2D systems in correlated materials.
