On the one hand, the results of tsunamis and storm surges are the same for human purposes and probably the same in the sedimentary record. When we look for ancient tsunamis, the historical record is ambiguous. Some of history's most deadly tsunamis might have been storm surges. History mentions very deadly "tidal waves" along the South Asian coast, comparable to what we're seeing in Myanmar, and for planning purposes we need to beware both earthquakes and storms.
On the other hand, for geology the two causes must be distinguished, if possible. In some places, such as the American Gulf coast, there are no earthquakes, and the prehistoric hurricane record can be deciphered by experts in paleotempestology. But if the Myanmar cyclone had happened a thousand years ago, could we tell from the sediments what had happened? Hard to say. Without sure signs of earthquake such as sand blows or suggestive signs like mud volcanoes, we're stuck.
But probably arguing about "tidal waves" versus "tsunamis" is immaterial, just as it is when the press talks about the "Richter scale" for earthquakes. The important thing is that geologists get to explain Earth hazards to the public.