Okay, so not all schools have it, but you can def apply early to all schools? Or do some schools make you wait until a certain deadline to submit apps?
You can (and should) apply early to all schools; no schools make you wait until a certain deadline. However, you won't be able to submit apps until the current year's apps become available (somewhere around September/October), so I guess you could say that schools make you wait until the apps are available.
Now, the thing to keep in mind, though, is that, although you can apply early (albeit not EA or ED) to all schools, you may not hear back from them for a while. This may be for any number of reasons (i.e., they want to compare your app with others as more come in, they don't start reviewing apps until a certain date, etc.), but it's good to keep in mind that even if you submit your apps early in the cycle, you might not hear back from schools for a few months.
Okay...are my chances better if I apply early admission or early decision than if I just submit my stuff in early?
That's a good question. The answer is not cut-and-dry. Arguably, you could definitely get a bump by telling schools that they are your first choice, i.e., applying via Early Action or Early Decision. However, there are enough people out there that do so that the effects might not be as huge as you'd like. Historically, though, most schools have let in a higher percentage of binding ED/EA applicants than the regular decision applicants. Now, regarding just submitting your materials early--that definitely gives you a slight bump over other regular decision applicants, although not a huge one. It basically boils down to the fact that the earlier you apply, the more seats are available in the class, which increases your chances of acceptance.
Applying EA/ED can definitely give you better chances than just submitting materials early. However, you still have to submit a good app with great credentials for that to really be the case. A poor app will yield the same results regardless of when you apply or how you apply in the cycle.
Okay...that makes sense. But my numbers still have to be as good if not better than the medians for my chances to be really good.