The core product is NOT the tangible, physical product. It is not touchable. That's because the core product is the BENEFIT of the product that makes it valuable to the customers. So with the car example, the benefit is convenience, i.e. the ease at which one can go where he likes, and when he want to. Another core benefit is speed since one can travel around relatively quickly.
The actual product is the tangible, physical product. One can get some use out of it. Again with the car example, it is the vehicle that one might test drive, buy and then collect.
The augmented product is the non-physical part of the product. It usually consists of lots of added value, for which one may or may not pay a premium. So when one buys a car, part of the augmented product would be the warranty, the customer service support offered by the car's manufacturer, and any after-sales service.