A tsunami is a wave that is created by an earthquake under the ocean. A vertical slip sets up the wave which travels through the full depth of the ocean. As the ocean shallows at the coast, the wave is compressed and forces the water to rise to create the devastating wave that rushes onto the shore. A storm surge is created by the very high winds in hurricanes/typhoons/tropical cyclones. There is a rise in sea level caused by the winds but this is only at surface level. It is not through the full depth of the ocean like a tsunami. A storm surge arriving on a high tide can raise sea levels by two metres or so above the high tide.