Maybe the terms need to be defined. This paper is very helpful: https://www.nccih.nih.gov/health/complementary-alternative-or-integrative-health-whats-in-a-name

Alternative medicine is the use methods not considered mainstream by modern medicine - "detox" would fall into this category, as would more common practices as massage therapy, acupuncture and herbal medicine. Some of these have a very long history across cultures, others are more recent and can be controversial.

Complementary medicine it the use of conventional and alternative medicine therapies together. For example, my pain management program which combines medication, myofascial release, massage and exercise.

There are MANY things to be learned and valued from both conventional and alternative practices, so it makes sense to integrate them for the best possible outcome.

Another caveat: only some alternative practices and substances are regulated in any way. To me that means "Buyer Beware" - as @lindes pointed out, detox has been largely found to be ineffective, and doesn't come without risks: https://www.nccih.nih.gov/health/detoxes-and-cleanses-what-you-need-to-know

Finally, a word about supplements, which are often part of alternative practices. Supplements are not regulated by the FDA, may be sold on-line, in health food, grocery and drug stores, even in gas stations and dollar stores. Some are touted as miracle cures for anything from baldness to cancer. Sometimes the ingredients are not even disclosed on the label, or have made-up names that are proprietary. Always make sure you know exactly what is in a supplement and how each ingredient may interact with your conditions or medications. (You can look here:https://www.webmd.com/vitamins/index ) Buy from a reputable source and brand, not the cheapest one - look for products certified by an independent lab, with the name of that lab on the label. And beware of anything you can only find on-line or on TV sold by the maker/promoter.

Does this help?
Sue