Electronic structure calculations for a homo-material semimetal (thick Sn)/semiconductor (thin Sn) heterodimensional junction and two conventional metal (Ag or Pt)/silicon hetero-material junctions are performed. Charge distributions and local density of states are examined to compare the physics of junctions formed by quantum confinement in a homo-material, heterodimensional semimetal junction with that of conventional Schottky hetero-material junctions. Relative contributions to the Schottky barrier heights are described in terms of the interface dipoles arising due to charge transfer at the interface and the effects of metal induced gap states extending into the semiconducting regions. Although the importance of these physical mechanisms vary for the three junctions, a single framework describing the junction energetics captures the behaviors of both the heterodimensional semimetal junction and the more conventional metal/semiconductor junctions.