Hexagonal and arrow-headed ZnO nanorod structures have been grown by low pressure chemical vapour deposition (CVD) and atmospheric pressure metal-organic CVD. The technology ensures a high optical quality of the produced nanostructures to act as gain medium for stimulated emission in the ultraviolet spectral region in combination with high quality factor laser resonators. Multiple sharp lasing peaks related to the guided modes were realized from single hexagonal nanorods and arrays of hexagonal ZnO nanorods. A comparative analysis of the variations of lasing spectra from shot to shot of pumping, and the dependence of lasing threshold on the area of pump beam spot on the sample surface in disordered agglomerations of hexagonal nanorods and in layers consisting of arrow-headed nanorods, demonstrate that lasing is determined by the superposition of guided modes in the first case, while random lasing occurs in the second case.