Two-dimensional (2D) heterostructures composed of transition metal dichalcogenides (TMDCs) are promising materials for next-generation electronics and optoelectronics due to their unique electronic and optical properties. Although 2D TMDC heterostructures with coexisting vertical and lateral junctions are highly desirable for both fundamental research and technological applications, they have rarely been explored. Here, we report for the first time the synthesis of 2D heterostructures with coexisting vertical and lateral junctions composed of MoSe2 and WSe2. Monolayer MoSe2 is first synthesized on a substrate due to its lower thermodynamic formation energy followed by the growth of monolayer WSe2 on both the basal plane and edges of MoSe2, thereby forming MoSe2-WSe2 heterostructures with coexisting vertical and lateral junctions. These heterostructures are characterized using various analytical techniques. We investigated nonlinear optical (NLO) properties using harmonic generation measurements to determine the crystal orientation of star-shaped MoSe2-WSe2 heterostructures. In addition, we investigated the junction geometry-dependent NLO responses of the vertical and lateral heterojunctions over a broad spectral range to demonstrate their resonant features and interlayer coupling effects. Furthermore, we fabricated electronic devices using these heterostructures and compared the diode characteristics of the vertical and lateral p-n junctions. These MoSe2-WSe2 heterostructures with coexisting vertical and lateral junctions are advanced materials for 2D electronics, optoelectronics, and nonlinear optical applications.