The interstellar medium (ISM) is turbulent on all scales and in all phases. In this paper, we study turbulence with different tracers in four nearby star-forming regions: Orion, Ophiuchus, Perseus, and Taurus. We combine the APOGEE-2 and Gaia surveys to obtain the full 6-dimensional measurements of positions and velocities of young stars in these regions. The velocity structure functions (VSFs) of the stars show a universal scaling of turbulence. We also obtain Hฮฑ gas kinematics in these four regions from the Wisconsin H-Alpha Mapper. The VSFs of the Hฮฑ are more diverse compared to the stars. In regions with recent supernova activities, they show characteristics of local energy injections and higher amplitudes compared to the VSFs of stars and of CO from the literature. Such difference in amplitude of the VSFs can be explained by the different energy and momentum transport from supernovae into different phases of the ISM, thus resulting in higher levels of turbulence in the warm ionized phase traced by Hฮฑ. In regions without recent supernova activities, the VSFs of young stars, Hฮฑ, and CO are generally consistent, indicating well-coupled turbulence between different phases. Within individual regions, the brighter parts of the Hฮฑ gas tend to have a higher level of turbulence than the low-emission parts. Our findings support a complex picture of the Milky Way ISM, where turbulence can be driven at different scales and inject energy unevenly into different phases.