Monolayer MoS2 in triangular configurations with rich edges or high-quality uniform films are either catalytically active for the hydrogen evolution reaction or flexible for functional electronic and optoelectronic devices. Here, we have experimentally discovered that these two types of MoS2 products can be selectively synthesized on graphene or sapphire substrates, which are associated with both different adsorption energy and diffusion-energy barrier for vapor precursors during growth. Our study not only provides insights into the on-surface synthesis of high-quality MoS2 monolayers, but also can be applied to the growth of vertically-stacked and large-scale in-plane lateral MoS2-graphene heterostructures.