I've come across articles say their software will run on tp-link hardware that is ar71xx for example then comments from people saying they are running it on ar9xxx based hardware for example.
I am not understanding. Does this mean that any arxxxx stuff will run the same firmware/packages? How can I learn more about this to understand what runs on what.
Yes, but it's better to use the packages manager if you do not understand the CPU/Architecture breakdown. Also, you can access the package folder on the same downloads page where you access the firmware.
Each supported devices lists its CPU and Target Architecture. If you are trying to support a device not listed, you will have to be willing to open the router to get that information.
I use the package manager but many projects offer their own downloads which are not in the supported packages, one off custom builds. I did look at the toh but first need to have a clue about what I asked as a starting point. I am not trying to support anything but to understand when certain packages will run on other hardware.