This may not be the best input, but I'll play. Tell them a number of terms out there probably represent "fast attack". But it's really all about the concept of fast attack. Think of any battlefield, ours or other types, and there may be opportunities (or needs) to get into harm's way to save people or stop a fire when it's at a stopping place. Today this has been influenced somewhat by safety concerns, like "2in 2out". Second to safety, the Fireground decision maker must appreciate the water supply aspect to all this. "Fast Attack" has value if there is good reason, like someone is seen in the window. It has no professional value if the reason was to boast about "first water" on the fire. Some fast attack images would be getting a line in to control an egress point for evacuees, or getting at it while small and possible. That one meaning we can get it off the tank, as opposed to securing a continuous supply. I know one Department that once used the tank tactic (fast attack), while the Engineer did a Reverse to a hydrant. They got a shock one night when the plug was dry, and the Engineer had to lay out again. Yep, the attack crew came out when the water stopped!
So think of these thoughts if it helps. Rapid intervention (fast attack) is thought of today as a concept of rescuing our own Force. But it has long been used by our Service, often to describe apparatus designed to get things started before other resources arrive. Most agencies think of any of the Companies operating like this when First In. But Airports and even some municipal agencies have set up Companies to perform this way as routine. Locally to me, some Departments once operated two piece Companies, with a fast attack or "Booster" rig getting on scene first, while their pumper focused on water. This works when it works, meaning both pieces are depending on the other in this arrangement. When one is not available, the other is severely restricted from full capability.