Well, of course, they are different from each other. And generally speaking, eye stye is caused by some bacteria and allergies. So for the treatments, you should make sure your eyes are far from the bacteria, so that they can not be infected. Also, burning eyes will be the symptom, so you can just have heating a piece of garlic, which will work wonders if done right. On the other hand, a hordeolum is a small infection of the glands in the eye, which are located in the eyelids. And then, because of the infection, a red bump on the eyelid which looks like a pimple will occur. For the treatments, you can just try some tea bag, which contains many different objects which do a good job to stye.