Think of “storm surge” as a wind driven tsunami with wind driven waves - depending on the circumstance and location, big waves - on top of it.
VERY good info. & graphics here:
https://www.nhc.noaa.gov/surge/
Note that the storm surge is mostly wind driven (not pressure driven), so if the storm stalls and winds blowing onshore stay up, the surge stays up too (although tides in and out also affect the total height of the water.)
The onset of an earthquake driven tsunami is more sudden, often preceded by a retreat of the waters first, and there are often multiple inundations and retreats. Absent human communication, there may be very short warning, if any, as earthquake tsunamis can travel rapidly far from their source. With storm surges you pretty much see them build as the storm builds. Ultimately, certain earthquake and volcanic tsunamis can be higher (I think - someone correct me if wrong), to say nothing of asteroid hit tsunamis, but, storm surges have those pounding waves that can in combination go on for many hours.
Thank you very much...I do appreciate it - makes me smarter than I was before I sat down at the computer and FR...