Although many prototype devices based on two-dimensional (2D) MoS2 have been fabricated and wafer scale growth of 2D MoS2 has been realized, the fundamental nature of 2D MoS2-metal contacts has not been well understood yet. We provide a comprehensive ab initio study of the interfacial properties of a series of monolayer (ML) and bilayer (BL) MoS2-metal contacts (metal = Sc, Ti, Ag, Pt, Ni, and Au). A comparison between the calculated and observed Schottky barrier heights (SBHs) suggests that many-electron effects are strongly suppressed in channel 2D MoS2 due to a charge transfer. The extensively adopted energy band calculation scheme fails to reproduce the observed SBHs in 2D MoS2-Sc interface. By contrast, an ab initio quantum transport device simulation better reproduces the observed SBH in 2D MoS2-Sc interface and highlights the importance of a higher level theoretical approach beyond the energy band calculation in the interface study. BL MoS2-metal contacts generally have a reduced SBH than ML MoS2-metal contacts due to the interlayer coupling and thus have a higher electron injection efficiency.