It's easy to see why some people might think that Crossfit and HIIT are the same thing. After all, both involve doing different types of activities within a workout. But CrossFit has HIIT and a little more. It uses things like gymnastics and Olympic weightlifting movements, making it a great extension of HIIT workouts.
CrossFit is a trademarked training methodology that combines elements of strength, endurance, gymnastics and interval training. It usually lasts around an hour and is divided into four different sections. A MetCon, or metabolic conditioning training called AMRAP, is a fairly common CrossFit workout. This type of high-intensity interval training can be done in home training sessions as well.
On the other hand, cross-training is simply a term that people use to talk about exercise that is not directly related to the sport or activity they have chosen. Resistance training is great for building muscle, increasing basal metabolic rate, which can improve fat burning and increase bone density. Cross-training allows athletes to continue exercising around their injury so they can maintain their fitness while they're on the sidelines. If you're looking for a training program that takes you out of your comfort zone and encourages you to try new things, you'll find it at CrossFit.
It's also important to note that doing CrossFit alone is not necessarily cross-training. A study published in the Journal of Obesity discussed how “the effect of regular aerobic exercise on body fat is negligible and how other forms of exercise, such as interval training, were more effective in changing body composition. So if you're ready to start a training plan and haven't maintained good physical shape for some time, HIIT training is a great place to start. But if you're ready to try harder and build on the foundation you've developed, Crossfit would be a fun challenge and could also guarantee results.