What is a "differential chemical abundance"?
If the line emission is optically thin, then the measured line flux is proportional to the abundance $F_{\nu} \sim n$ of a species along the line of sight (if it's only one species).

The problem here is that $F_{\nu}$ needs to be measured relative to a baseline. If that fails, e.e. when the stellar signal is too noisy, one doesn't know what this should be. But a measurment at two different wavelengths $\nu$ and $\nu'$ that lie reasonably close together, can at least yield a difference in abundances $F_{\nu}-F_{\nu'} \approx n-n'$ relative to this unknown base level.
This allows then to construct an atmospheric model, up to the unknown base level, which one can try to fix with other physical arguments.