Shore: 'the land along the edge of a sea, lake, or other large body of water.' Beach: 'a pebbly or sandy shore, especially by the sea between high- and low-water marks.' Coast: 'the part of the land adjoining or near the sea.' They are all synonyms for each other, beach is where you would go to swim on a hot day, coast refers more to the edge of land (with cliffs, rocks, caves etc.) that meets sea, shore is less frequently used word for beach or something similar.

Simply semantics. All three mean ocean or bay front property. However, people that live away from these areas will often say "Were going to the shore" meaning we are going to an area where there is a beach. The coast is generally spoken of a larger area such as the east coast meaning the area stretching from Maine to Florida where the ocean touches the land. The Beach is somewhere you go to play. However, all mean the same thing. Just said differently in different areas of the country (US)