Originally Posted by ChrisSlicks

Play would be any movement that isn't rotation. Jack that corner off the ground slightly and shake the wheel in all directions. There shouldn't be any wheel movement other than the steering moving a bit. It would feel like a click if bad.

Run-out is taking a measurement against the wheel at a fixed location, while the wheel is slowly rotated. The gap measurement should remain pretty constant. Think of spinning a bicycle wheel and having it randomly rub against the brake pad each rotation, that is run-out. In the case of a wheel it would mean that either the wheel is not correctly seated against the hub due to an imperfection, rust, or a bent or loose hub assembly.