Storm surges are caused when strong winds push seawater towards the coast. Humanity has been witnessing the flooding phenomenon ever since civilization began. There are different types of flood; for example slow river floods, lake floods, flash floods, river floods, rain floods, and coastal floods. Apparently coastal floods are by far the most terrifying of all floods due to their colossal scale and the destruction they bring along. Although a storm surge plays a vital part in bringing about of floods yet it is not the only factor or a factor which entirely on its own could cause flood.
A Lake flood is a kind of flood where storm surge does not play a prominent role. Mostly lakes obtain their water by means of rains or melting of ice from mountaintops. Excess of rain or ice melting can cause rivers to fill up very rapidly and sometimes overfill as well. Rising of water in rivers do not have much to do with storm surge; and even if a storm strong enough hits the water, there has to be an adequate amount of water present in the lake for it to cause potential flood. The water levels of lakes fluctuate highly by rains and surrounding meltdowns; however a storm surge can increase the probability of water getting out of its usual track when sliding down from mountaintops.
Slow river floods occur when the water exceeds the amount that the river can hold. These floods are relatively easier to predict, hence less destructive. Storm surges in a slow river flood can increase the possibly of a quicker flood as well as an unpredictable one. Although just as in the lake floods, storm surges solely cannot cause flooding in this scenario.
Storm surges play a more central role in coastal floods. Constant high levels of wind above oceans persistently push seawater towards the coast. Storm surges developed in the form of cyclones or hurricanes above deep oceans. Storm surges are often responsible for the majority of deaths from tropical cyclones as well. However, a storm surge usually does not succeed on its own in causing flood. Usually enormous destructions, such as the Tsunamis, are caused by deep water earthquakes. Underwater earthquakes are highly hazardous because they totally shake-up the whole routes of seas and oceans. Underwater earthquakes do not necessarily give rise to the sea levels but simply quake the water to an extent where water reaches to an unbelievably dangerous speed and thus cause floods in regions near the coast. The strong force of moving seawater can quake the ground as well as foundations of manmade structures causing a lot more destruction than slow river foods or lake floods. So on the whole, a storm surge alone does not cause coastal floods but indeed a combination of earthquakes, sea tides, and sea storms, give birth to coastal floods.
Sources:
http://www.bbc.co.uk/weather/features/understanding/1953_flood.shtml
http://www.mnn.com/earth-matters/translating-uncle-sam/stories/floods-when-water-attacks
http://www.nhc.noaa.gov/HAW2/english/storm_surge.shtml