Everest is the mountain whose summit attains the greatest distance above sea level. Several other mountains are sometimes claimed as alternative "tallest mountains on Earth". Mauna Kea in Hawaii is tallest when measured from its base; it rises over 10,200 m (6.3 mi) when measured from its base on the mid-ocean floor, but only attains 4,205 m (13,796 ft) above sea level.
By the same measure of base to summit, Denali, in Alaska, is also taller than Everest.
quote: good old Wikipedia
In this context, height is measured from sea-level, whilst how tall a mountain is, is measured from its actual base, which could be miles down in the ocean.