We investigate the relationship between the variability of broad absorption lines (BALs) or narrow absorption lines (NALs) and that of continuum using a dataset of two-epoch SDSS spectra containing 134 C\,{\footnotesize IV} NAL-BAL pairs. Our analysis reveals an anti-correlation between the fractional equivalent width (EW) variations in NALs (or BALs) and the fractional flux variations of the continuum, with Spearman rank correlation coefficients of $r$ = -0.47 ($p$ = 1E-08) and $r$ = -0.58 ($p$ = 1E-13), respectively. In addition, we find a positive correlation between the fractional EW variations in NALs and BALs ($r$ = 0.72, $p$ = 1E-22), and derive a regression equation $\Delta \mathrm{EW_{NAL}} / \langle\mathrm{EW_{NAL}}\rangle = 0.803\Delta \mathrm{EW_{BAL}} / \langle\mathrm{EW_{BAL}}\rangle + 0.008$, with an intrinsic scatter of 0.14. These results suggest that the variability in the ionizing continuum may play a significant role in the observed changes in C\,{\footnotesize IV} NALs and BALs, supporting the idea of photoionization-driven variability. The co-variability between C\,{\footnotesize IV} NALs and BALs may imply that they originate from outflows with similar physical conditions (e.g, high ionization state).