Original: The original name for Fatah's armed wing was al-Assifa (The Storm), and this was also the name Fatah first used in its communiques, trying for some time to conceal its identity. This name has since been applied more generally to Fatah armed forces, and does not correspond to a single unit today.
Simplified: Leaders of Fatah have said they did not create the brigades, or make them the military of Fatah.