Doing harm and allowing harm concern an agent’s relationship to a harmful process. They do not map neatly onto moving versus staying still: an action can allow an existing threat to continue, and an omission can be part of causing harm. Intention and causal responsibility are separate dimensions.
The distinction is harder than separating movement from inaction. A person can cause harm by failing to perform an assigned safety check, while someone actively stepping aside may allow an independently developing danger to continue. To analyze a case, identify the threat’s causal history, the agent’s involvement, and any special duty to intervene. Keeping these features separate makes it possible to ask whether doing and allowing differ morally when other relevant considerations are held steady.