We present a comparative study, combining density functional theory with scanning tunneling microscopy/spectroscopy, of two aromatic molecules bonded with a variable number of Cu adatom(s) on a Cu(111) surface. The two molecules, 1,3,5-tris(pyridyl)benzene (TPyB) and 1,3,5-tris(4-radical-phenyl)benzene (TPB), possess the same aromatic backbone but bond weakly versus strongly to Cu with different terminal groups, respectively. We find that TPyB and TPB exhibit, respectively, small versus large charge transfers between the surface and the molecule; this contrast results in opposite shifts in the calculated density of states distributions and thus explains the opposite STS peak shifts observed in our experiments. The two molecules exhibit weak donor versus strong acceptor characters. This work provides a fundamental understanding, on a single-molecule level, of the principle that selecting specific functional groups can effectively and intentionally modify the molecular electronic properties in a wider class of molecule-metal interfaces.