The coast is the area of land which lies alongside the sea. When you talk about a coast, you may mean just the land close to the sea, or a wider area inland.

1. To the north and south the coast is rock for the most part.
2. At this time sea kale was a relatively common plant around the coasts.
3. …a protest at official plans to site a third London airport on the Essex coast.

A beach is a flat area immediately next to the sea that is usually covered in sand or pebbles.

4. Tourists go there to walk on the beach.
5. Gradually the oil stains were cleaned from the beaches.

The shore is the area of land along the edge of the sea, a lake, or a wide river.

6. Bronzed men surfed into the shore on curling waves.
7. We could see the trees on the other shore.