Smaller squat racks are often referred to as “half racks”. They have a number of advantages, such as saving on space, and a lower price tag than a full power rack, but they offer slightly less flexibility in the number of exercises you can use them for. Some people also prefer smaller squat racks because they can feel less restrictive.
The squat stand is an even more stripped down version. They’re even more affordable and space-efficient, but typically won’t have any extra features beyond the basics.
Power racks are the larger, more advanced racks out there. They can be used for a whole range of weightlifting exercises, like deadlifts, heavy rows, shoulder presses and more, and offer a number of safety features and storage options, but they also tend to take up a lot more space.