While the multiband compressor is a compressor that incorporates some elements of an EQ, a dynamic equaliser can be thought of as an EQ with elements of a compressor. A dynamic equaliser can boost a signal when its level exceeds an adjustable value in the respective frequency range. It also works the other way around and allows for attenuating a signal, provided that a selectable level is undercut. And the detector band and EQ band do not even have to be the same …
It can get pretty complicated, but the dynamic EQ is a very powerful tool. After all, why would one want to boost the entire treble range to carve out a hi-hat, even when the instrument is not playing? A dynamic EQ only operates when there is material to process. Even between two eigths notes of the hi-hat, it will remain inactive and leave other signals like vocals, guitars and snare drum unaffected.