The in-plane graphene/hexagonal boron nitride (Gr/h-BN) heterostructures have received extensive attention in recent years due to their excellent physical properties and the development potential of next-generation nanoelectronic devices. Generally, different bonding types between Gr and h-BN are considered in different non-equilibrium molecular dynamics (NEMD) simulations studies. However, which type of bonding is most conducive to interface thermal transport is still very confusing. In this work, we investigate the interfacial thermal conductance (ITC) and the thermal rectification (TR) in five different bonding types of in-plane Gr/h-BN heterostructures by using NEMD simulations. It is found that the ITC depends strongly on the bonding strength and arrangement of different atoms across the boundary. Among the five different bonding types of heterostructures, the C-N bonded heterojunction exhibits the highest ITC due to its stronger interfacial bonding. The analyses on the strain distribution indicated that a low interfacial stress level at the interface junction, may facilitate the heat conduction, thus leading to a higher ITC. In addition, we found that TR occurs in all five bonded heterostructures, and the C-B bonded heterojunction possesses the highest TR factor. The present study is of significance for understanding the thermal transport behavior of Gr/h-BN heterostructures and promoting their future applications in thermal management and thermoelectric devices.