LAeq and LAIeq are both A-weighted, time-averaged values, but on a different basis. The LAeq is normally based on a non-time-weighted momentarily level, whereas the LAIeq uses the impulse-weighted LAI level.
In earlier days, where only LAS or LAF results were available, the LAeq cacluation was based on these results. Looking at the time-averaged level for a multiple of the time-constant (a couple of seconds), LAFeq will not be different from LASeq and the following applies: LAeq = LASeq = LAFeq.
In contrast, LAIeq is normally higher at impulisve noise than LAeq. (LAIeq > LAeq)
For constant noise, LAIeq = LAeq applies.