Ledge is a narrow horizontal surface/shelf projecting from a wall, cliff, other surface. Edge is the outside limit of a surface. So, you could have the edge of a ledge. You can get onto a window ledge. You can climb onto a ledge jutting out from a cliff. But if you are on top of the cliff, your Mom would say: "Don't go near the edge" - this is the outermost part of the top of the mountian. Any further, and you would fall. You can have the edge of a cup. Or of a bed. Hope that assists

An edge (used in the context asked) is the corner or the boundary of something. Examples: Don't stand close to the edge of the cliff or you will fall. She had a house on the edge of the town. A ledge is like a shelf or a platform that sticks out from the side of a building or cliff or a vertical surface. The ledge was just wide enough for her foot to fit fully. He eased himself along the ledge to reach the terrified boy.

See here: - https://www.oxfordlearnersdictionaries.com/definition/english/edge_1?q=edge and here: - https://www.oxfordlearnersdictionaries.com/definition/english/ledge?q=ledge Cheers!