Why does a boat at sea experience a tsunami differently from a boat near the shore?

A tsunami is a wave with an amplitude of a meter or so, that can go as fast as 700km/hr in the open ocean (the speed of an airplane). When a boat is at deep sea, a tsunami just seems like a normal wave which has no effect on the boat itself. It is only when the tsunami reaches the shallow waters near the coast that it gets a destructive impact: the wave sort of piles up and gains in height. A boat near the coast will then be carried inland like anything else onshore.