A short circuit is the electrical event. An arc flash is a hazardous byproduct that can happen when that event doesn't stay a clean metal-to-metal fault — and its severity depends on more than just how much current is available.
The two terms get used together so often — "arc flash from a short circuit," "short-circuit and arc-flash study" — that it's easy to lose track of which one is the cause and which one is a possible consequence. A short circuit doesn't always produce an arc flash, and the arc-flash hazard from a given fault current isn't fixed — it depends heavily on a variable most people overlook entirely.