A legal cause (sabab) provides a recognized route to a ruling; an operative cause ('illah) is the effective rationale linked with the ruling; a condition (shart) is required for its realization even where it does not itself generate the ruling.
The arrival of prayer time and the requirement of purity for valid prayer represent different legal relationships. Establishing that a cause exists does not show that every necessary condition is fulfilled.
In questions of direct action, indirect causation, liability for property and conditional legal acts, these distinctions become especially important. What brings a legal question into operation is not invariably the effective feature or the condition of validity.
Ask which event activates the duty, which feature grounds it, which condition is required and whether an impediment exists.