The optical vortex (OV) and spatiotemporal optical vortex (STOV) are special beams carrying different forms of orbital angular momentum (OAM). OV has longitudinal OAM, while STOV has transverse OAM and is coordinated with time to achieve control. Due to their reliance on different physical mechanisms, traditional optical platforms are difficult to independently control these two vortex beams on the same platform, which to some extent limits the understanding of the unified physical mechanism of spatial and spatiotemporal orbital angular momentum and hinders the development of multi-dimensional light field manipulation technology. This paper proposes a terahertz (THz) metasurface device based on vanadium dioxide (VO₂) phase change material, integrating the in-plane asymmetry (provided by triangular pores) required to excite STOV and the anisotropic phase units (realized by VO₂ broken rings) required to generate OV into one metasurface platform, enabling the dynamic switching of OV and STOV on the same metasurface platform. The uniqueness of its design and the key to achieving functional integration lies in the selection of Si and VO₂ materials on the upper layer of the metasurface. When VO₂ is in the insulating state, its dielectric constant in the THz band is similar to that of Si and its conductivity is very low. Different rotation angles of the units can still be considered as a periodic structure with the same symmetry on a macroscopic scale. The structure uses circularly polarized waves for reflection, generating a topological dark point at approximately 1.376 THz and a topological dark line between 1.3765 THz and 1.378 THz, exciting STOV. When VO₂ transforms into a metallic state, its high conductivity makes the broken ring the dominant scatterer. By reasonably arranging the encoded units of the metasurface and combining the Pancharatnam-Berry (PB) phase, not only can OV with different topological charges be generated, but also multi-channel and multi-functional OV can be generated through convolution theorem and shared aperture theorem. Subsequently, the influence of structural parameters was analyzed in detail. By changing the shape of the triangular pores and the thickness of the broken ring, the two vortex beams were adjusted, and it was found that they have strong topological stability under different conditions and can be reversibly switched through temperature control. This research provides a new idea for realizing multifunctional vortex light generation in the terahertz frequency band and opens up new avenues for the application of vortex light in terahertz communication and optical information processing.