Alchemy, at the core, was about taking something and making it better. While there was the end goal, the focus was more on the process of discovery. Alchemists are progressive thinkers, no matter the branch they practiced. This leads into my next point that there are a lot of aspects in Alchemy that have nothing to do with each other and that is directly because each process was different. Expanded thought upon the last (not to mention that many Alchemists were solitary practitioners). To really get to know Alchemy, you have to look at the cultures the sources come from. Look at the art, the philosophy, the typical paridigms of each culture they are found in.
I would not take Wiki to be the last word on any topic, but this page is a good way to expose yourself to various aspects of Alchemy to figure out what you'd like to further research. I cannot explan the differences between each practice because they are not all branches I have studied (that's what you get with a topic as vast as this).