Context. The chemical evolution of pre-stellar cores during their transition to a protostellar stage is not yet fully understood. Detailed chemical characterizations of these sources are needed to better define their chemistry during star formation. Aims. Our goal is to characterize the chemistry of the starless cores C2 and C16 in the B213/L1495 filament of the Taurus Molecular Cloud, and to understand how it relates to the environmental conditions and the evolutionary state of the cores. Methods. We made use of two complete spectral surveys at 7 mm of these sources, carried out using the Yebes 40-m telescope. Derived molecular abundances were compared with those of other sources in different evolutionary stages and with values computed by chemical models. Results. Including isotopologs, 22 molecules were detected in B213-C2, and 25 in B213-C16. The derived rotational temperatures have values of between ∼5 K and ∼9 K. A comparison of the two sources shows lower abundances in C2, except for l-C3H and HOCO+, which have similar values in both cores. Model results indicate that both cores are best fit assuming early-time chemistry, and point to C2 being in a more advanced evolutionary stage, as it presents a higher molecular hydrogen density and sulfur depletion, and a lower cosmic-ray ionization rate. Our chemical modeling successfully accounts for the abundances of most molecules, including complex organic molecules and long cyanopolynes (HC5N, HC7N), but fails to reproduce those of the carbon chains CCS and C3O. Conclusions. Chemical differences between C2 and C16 could stem from the evolutionary stage of the cores, with C2 being closer to the pre-stellar phase. Both cores are better fit assuming early-time chemistry of t ~ 0.1 Myr. The more intense UV radiation in the northern region of B213 could account for the high abundances of l-C3H and HOCO+ in C2.