When things are not familiar it is easy to be confused. But then I suggest a bit different way of looking for parts. If you look at how the water flows through the reactor, it may make parts easier. The hangup with almost any parts list will be that the supplies one guy finds will not be the same another may find. So the way I would go is to start with the tubing you use on your filter (it may be different) and then start finding what you need to tie it to the filter housing you find ( it may also be different) .
No need to look for a 1/2" barb fitting if your tubing is 3/4"?
I often take all the parts I have on hand like the big stuff and then go to the store and stand there testing parts until I find the one that actually does fit what I want. It often is not what the parts list calls for me to use.
It is nice to have a parts list but keep in mind that those may not be the parts that work for you as you shop.