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A gravity dam is a common example of a Storage Dam.

By function, dams are classified as storage, diversion and detention dams. A gravity dam, which resists water pressure by its own weight, is usually built of masonry or concrete to impound a reservoir that stores water for irrigation, water supply and power, so it is the typical storage dam.

A diversion dam (weir or barrage) only raises the water level to divert flow into a canal. By material a gravity dam is a rigid dam, so 'Non-rigid Dam' is wrong, and although a gravity dam can be designed to let water flow over its crest, that is a special case, not its defining type.