The claim that "mountains on the ocean floor are higher than the tallest mountain on land" is a persistent misunderstanding rooted in how you measure "height."
Mount Everest: 8,848.86 m (29,031.7 ft) above mean sea level. Highest point on Earth's solid surface.
Mauna Kea (Hawaii): Summit 4,207 m (13,802 ft) above sea level. Tallest seamount—but most of it is underwater.
Mauna Kea: Rises ~10,210 m (33,500 ft) from its base on the Pacific seafloor (~6,000 m below sea level) to summit. > Everest's ~3,700 m base-to-summit (from Tibetan Plateau ~4,500 m).
Earth's equatorial bulge (radius 6,378 km vs. 6,357 km at poles) means Chimborazo, Ecuador (6,263 m / 20,548 ft) summit is ~2,168 m farther from Earth's center than Everest's.
Seamounts are underwater volcanoes that don't breach the surface. >100,000 exist >1 km tall. Mauna Kea is the tallest. Guyots are flat-topped seamounts (eroded, then submerged).
Pop-science headlines love "Everest isn't the tallest mountain!" but conflate elevation (geodetic standard) with relief (geomorphic) and geocentric distance (geophysical). Each metric answers a different question.
For aviators, surveyors, and treaty law: Everest is highest. For volcanologists studying edifice volume: Mauna Kea. For satellite orbit designers: Chimborazo. Context dictates the metric.