Forza is about damage, GT is about grip and taking the proper line.
Yes GT is realistic, you just think everything is over twitchy because you don't realize how fast you are going. I am hoping they will add adaptive blur to GT5 to help that.
That's how cars act, so no it's not a "crazy fashion". It's a VERY steep learning curve, it just throws you in there but once you get it you will love it.
They key is to drive like you're on the track, take the proper line at the proper speed, only brake when your going straight, don't slam the brakes you will sow down slower then if you ease into them, don't just go full throttle everywhere especially around corners. Did I mention taking the proper line?