Probably not as much as you might think, Lisa. SUVs are generally based on a hatchback or sedan, and – generalising again – they use the same engines and transmissions. As you’ve identified, they’re a bit taller, but they’re not always larger inside thanks to the sometimes larger suspension towers intruding into the cabin space.
You’ll often find extra gear such as plastic wheel-arch flares and bigger bumper bars but, usually, these are nothing more than visual additions to make the SUV look tough and butch. You’ll often find different tyres on the SUV version, too, but a bigger difference (and it’s becoming less and less common) is the addition of all-wheel-drive (most hatches are now front-wheel-drive) which adds weight and complexity and seems a bit odd since these are not off-road vehicles by any stretch of the imagination.
Meantime, the biggest difference between an SUV and the hatchback it’s based on? Usually the price-tag.