A detox is something you do, such as going on a special diet for a few days. Sometimes it's called a cleanse. Personally, I don't think there's much to detoxing, partly because I've never read anything specific about the toxins (as, what are they?) other than vague references to chemicals. Also because I've never seen any details about their metabolic breakdown. Here's what Wikipedia has to say:
https://en.m.wikipedia.org/wiki/Detoxification_(alternative_medicine)
The Herximer reaction ("herxing"), more properly the Jarisch-Herximer reaction, is an inflammatory response to the destruction of certain toxin-containing bacteria by antibiotics. These toxins (endotoxins) are inside the bacterial cells and released when they are killed. It's associated with syphilis and a few other infections, including Lyme disease. Again, here's Wikipedia:
https://en.m.wikipedia.org/wiki/Jarisch–Herxheimer_reaction
So they are different phenomena, unless your cleanse includes
Penicillium mold.