So far I came up with one example: Blast eruption of volcano makes small stones and pebbles, which could be carried by waves, rivers etc.
Erosion, as you state, involves the moving of material. This can happen due to the action of running water, the impact of water via waves on coastal environments, wind or glaciers dislodging grains of geological material irrespective of whether it is weathered or not. Landslides are another form of erosion.