Interesting question. The coast is the edge of the land - so if you looked at a map, you'd say 'The coast is very straight here'. You can also say 'I'm going to the coast', just meaning that you're driving till you get to the sea.
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shore: zone between low tide and high tide.
coast: zone between coastline to till where ocean related features are found.
coastline: line divides shore and coast.
beach: zone between low tide breaker line to coast line.