To deepen our understanding of the chemical properties of the Planck Galactic Cold Clump (PGCC) G168.72-15.48, we performed observations of nine molecular species, namely, ce{c-C3H}, ce{H2CO}, ce{HC5N}, ce{HC7N}, ce{SO}, ce{CCH}, ce{N2H+}, ce{CH3OH}, and ce{CH3CCH}, toward two dense cores in PGCC G168.72-15.48 using the Tianma Radio Telescope and Purple Mountain Observatory Telescope. We detected ce{c-C3H}, ce{H2CO}, ce{HC5N}, ce{N2H+}, ce{CCH}, and ce{CH3OH} in both G168-H1 and G168-H2 cores, whereas ce{HC7N} and ce{CH3CCH} were detected only in G168-H1 and SO was detected only in G168-H2. Mapping observations reveal that the ce{CCH}, ce{N2H+}, ce{CH3OH}, and ce{CH3CCH} emissions are well coupled with the dust emission in G168-H1. Additionally, ce{N2H+} exhibits an exceptionally weak emission in the denser and more evolved G168-H2 core, which may be attributed to the ce{N2H+} depletion. We suggest that the ce{N2H+} depletion in G168-H2 is dominated by ce{N2} depletion, rather than the destruction by CO. The local thermodynamic equilibrium calculations indicate that the carbon-chain molecules of ce{CCH}, ce{HC5N}, ce{HC7N}, and ce{CH3CCH} are more abundant in the younger G168-H1 core. We found that starless core G168-H1 may have the properties of cold dark clouds based on its abundances of carbon-chain molecules. While, the prestellar core G168-H2 exhibits lower carbon-chain molecular abundances than the general cold dark clouds. With our gas-grain astrochemical model calculations, we attribute the observed chemical differences between G168-H1 and G168-H2 to their different gas densities and different evolutionary stages.