I think you are on the right track. Think about a car that can go 'round a corner at ludicrous speed, but has no steering feel, so you can't tell what the front wheels are doing. Might understeer into a ditch at any moment with no warning. This same car is set up so that if you do manage to lose grip, it will first understeer, then as soon as the front regains grip it will viciously snap oversteer. That's a car with good grip but very poor handling.
Conversely you can have a car with skinny tires and low grip, but will do whatever you want it to, completely predictable, adjustable on the throttle or with left foot brake just as you please, neutral at the limit and relaxed in its reactions. That's a car with little grip but excellent handling.