While Hossein is correct: you grasp an idea, but grip an object.
Grasp can still be used with a concrete noun. e.g. something can be within your grasp but cannot be within your grip
While you can't grip an abstract noun, you can both grasp and grip a concrete noun.
With concrete nouns the two words can be used interchangeably.
You can grasp something but have no grip on it (if you try to hold it but it's slippy). If you grip something with your hand, you're also grasping it. Note: using grasp with a concrete noun always involves holding it with your hand(s)
The term grasp also implies the wrapping of the hand around something, whereas it's possible to grip something without making that motion. Tires grip the road, but they cannot grasp it.
When in doubt, it's save to use grip for a concrete noun and grasp for an abstract noun
It's a difficult one, but I hope I helped!