"n" is what the airplane is actually experiencing right now. The g-limit is the structural line it must never cross — and the V-n diagram is where the two meet.
Pilots and engineers use "g's" loosely, and that looseness hides a real distinction. Load factor, n, is a live, dimensionless ratio — the lift the wings are generating right now divided by the aircraft's weight, n = L / W. It changes every second of flight: it's 1.0 in straight-and-level flight, climbs past 2 in a steep turn, and can spike briefly during a gust or an abrupt pull-up. The g-limitis a completely different kind of number — a fixed structural design value, set once by the manufacturer and stamped in the type certificate, that says how much load factor the airframe is certified to withstand without permanent damage or failure. Load factor is a measurement of what's happening. The g-limit is a boundary on what's allowed to happen. Confusing the two is how pilots and engineers underestimate how close a hard maneuver actually came to a structural limit.