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.