Gold-catalyzed ZnTe nanowires were grown at low temperature by molecular beam epitaxy on a ZnTe(111) B buffer layer, under different II/VI flux ratios, including with CdTe insertions. High-resolution electron microscopy and energy-dispersive X-ray spectroscopy (EDX) gave information about the crystal structure, polarity, and growth mechanisms. We observe, under stoichiometric conditions, the simultaneous presence of zinc-blende and wurtzite nanowires spread homogeneously on the same sample. Wurtzite nanowires are cylinder-shaped with a pyramidal-structured base. Zinc-blende nanowires are cone-shaped with a crater at their base. Both nanowires and substrate show a Te-ended polarity. Te-rich conditions favor zinc-blende nanowires, while Zn-rich suppress nanowire growth. Using a diffusion-driven growth model, we present a criterion for the existence of a crater or a pyramid at the base of the nanowires. The difference in nanowire morphology indicates lateral growth only for zinc-blende nanowires. The role of the direct impinging flux on the nanowire's sidewall is discussed.