Clarifying the origin and the electronic properties of defects in materials is crucial since the mechanical, electronic and magnetic properties can be tuned by defects. Herein, we find that, for the growth of h-BN monolayer on Re(0001), the patching frontiers of different domains can be classified into three types, i.e., the patching of B- and N-terminated (BlN-terminated) frontiers, BIB-terminated frontiers and NlN-terminated frontiers, which introduce three types of defects, i.e., the "heart" shaped moire-level defect, the nonbonded and bonded line defects, respectively. These defects were found to bring significant modulations to the electronic properties of h-BN, by introducing band gap reductions and in-gap states, comparing with perfect h-BN on Re(0001) with a band gap of similar to 3.7 eV. The intrinsic binary composition nature of h-BN and the strong h-BN-Re(0001) interaction are proposed to be cooperatively responsible for the formation of these three types of defects. The former one provides different types of h-BN frontiers for domain patching. And the later one induces multinucleation but aligned growth of h-BN domains on Re(0001), thus precluding their subsequent coalescence to some extent. This work offers a deep insight into the categories of defects introduced from the patching growth of two-dimensional layered materials, as well as their electronic property modulation through the defect engineering.