It's not necessarily a binary thing. You can have gradual sea level rise punctuated with rapid inundation events. This is exactly what happened in the British

It's not necessarily a binary thing. You can have gradual sea level rise punctuated with rapid inundation events. This is exactly what happened in the British Isles when low lying Doggerland (between modern England and Denmark) was wiped out by a wave which was likely caused by an underwater landslide; that wave was in turn caused by the melting ice at the end of the ice age, which was otherwise causing gradual sea level increase.