Every now and then I've seen a blog post attempting to cover this topic and they always just seem to fall short. "There are two methods: individual and side." Please. Not only are there dozens of ways of doing initiative, but many of them are desperately in need of a proper name at this point.
But exhaustively cataloguing every method is unfeasible. There are so many games that have nearly identical methods but with just a teensy tiny little quirk. "Instead of rolling a d20, you roll a d10." Yeah, whatever. I'm not about to list every single one of those as an individual entry. Some degree of broad categorization is needed.
But you will quickly see that my system of categorization is... feeble. I have unfortunately not been able to divine some grand system of fundamental initiative typology, easily charted along 6 key axes or something like that. You'll come to see why pretty soon, and we'll circle back to that topic in the conclusion. I instead tried to order my categories by vaguely-increasing order of general unfamiliarity / difficulty to explain and understand. We'll see how it goes.