HIIT refers to a very specific and particular type of training, and it's possible to do interval training, or high-intensity training, without actually doing a real HIIT workout.
HIIT is a cardio session arranged as short bursts of very hard work. The whole point of high-intensity training is to kick up the intensity of your cardio. In order to qualify as true HIIT, you'll need to push yourself to the max during every set. That's why they're short—anywhere from 20 to 90 seconds, typically.