The unusual tunneling effects of massless chiral fermions (mCF) and massive chiral fermions (MCF) in a single layer graphene and bilayer graphene represent some of the most bizarre quantum transport phenomena in condensed matter system. Here we show that in a two-dimensional semiconductor with Rashba spin-orbit coupling (R2DEG), the real-spin chiral-like tunneling of electrons at normal incidence simultaneously exhibits features of mCF and MCF. The parabolic branch of opposite spin in R2DEG crosses at a Dirac-like point and has a band turning point. These features generate transport properties not found in usual two-dimensional electron gas. Albeit its p Berry phase, electron backscattering is present in R2DEG. An electron mimics mCF if its energy is in the vicinity of the subband crossing point or it mimics MCF if its energy is near the subband minima.