The following video is quite good at explaining why outright grip is different from handling. I've been telling customer and students that for years:

So many people only care "how many G will it pull" when that's not really indicative of how the car actually behaves. Handling is a mix of lots of things, and the term for me is very broad. How a car handles incorporates not only grip, but also stability, predictability and balance as well.

The presenter of the video (who is a world-class Sports car racer in things like Porsche 962's) is dead on when he describes "handling" and how it can be subjective.

Also some other notes from the video. You'll notice in the slalom test (which is something us autocrossers are always doing) the car that gets all sorts of stupid is just flopping about like a dying fish. The cars that do better are much better damped and the roll rate is very much controlled. That's one reason I'm always going on and on about shocks being so important.

You can see in these video's how hard I can drive cars setup to be flogged:

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That is a car that handles. And on a skidpad the car can pull even more grip than what you see for values in the video. As was pointed out a skidpad is not exactly real-world driving, we do not drive in big smooth 200-300' circles, we have to turn, accelerate, stop.... and blend those things together.

I just thought you guys might like to see the video, and frankly it is a great way to show/explain my personal thinking when setting up a car.