herbal therapy vs botanical medicine

herbal therapy and botanical medicine both are nouns.

Word	Noun	Adjective	Verb	Adverb
herbal therapy	Yes	No	No	No
botanical medicine	Yes	No	No	No

As nouns, herbal therapy and botanical medicine are synonyms defined as:

herbal therapy and botanical medicine: the use of plants or plant extracts for medicinal purposes (especially plants that are not part of the normal diet)

Other synonyms of herbal therapy include phytotherapy.

herbal therapy (noun)	botanical medicine (noun)
the use of plants or plant extracts for medicinal purposes (especially plants that are not part of the normal diet)	the use of plants or plant extracts for medicinal purposes (especially plants that are not part of the normal diet)