Per Oxford Dictionary of Earth Sciences: Seamounts are isolated, submarine mountain rising more than 1000m above the ocean floor. The sharp, crested summits of seamounts are usually 1000-2000m below the ocean surface. Seamounts are of volcanic origin.
Per kaberett: To avoid classifying seamounts by arbitrary sea level (dependent on availability of surface water), the key point is then that seamounts are features of volcanic origin that rise over 1000m above oceanic crust.
Per Wikipedia: A seamount is a mountain rising from the ocean seafloor that does not reach to the water's surface (sea level), and thus is not an island.
Per Oxford Dictionary: Submarine means "Existing, occurring, done, or used under the surface of the sea."
Per NOAA: A seamount is an underwater mountain on the seafloor.
Are all seamounts below the water, or do they include formations that rise above the water?
UPDATE: Atolls not within the scope of defining formations that rise above the water; meaning atolls are atolls, and not seamount crests.