We report on the growth, cathodoluminescence and micro-photoluminescence of individual radial and axial CdTe insertions in ZnTe nanowires. In particular, the cathodoluminescence technique is used to determine the position of each emitting object inside the nanowire. It is demonstrated that depending on the CdTe deposition temperature, one can obtain an emission either from axial CdTe insertions only, or from both, radial and axial heterostructures, simultaneously. At 350 °C CdTe grows only axially, whereas at 310 °C and 290 °C, there is also significant deposition on the nanowire sidewalls resulting in radial core/shell heterostructures. The presence of Cd atoms on the sidewalls is confirmed by energy dispersive X-ray spectroscopy. Micro-photoluminescence study reveals a strong linear polarization of the emission from both types of heterostructures in the direction along the nanowire axis.