Lets remember also that healers, mainly female, ended up being classed as witches once upon a time. Most didn't practice magickal arts. They merely had the knowledge of which root, herb, or plant helped ease which condition. They had an understanding of how the body worked. To be perfectly honest, it seemed in many situations the healers treatments were more effective than what was classed as conventional medicine. Think about it, bleeding a sick person is not a very good idea, and some died from the treatment alone.
Now technically, both are forms of medicine. Medicine is a science, but due to the split ages ago with the disagreeing theories and practices of treating patients, one was labeled as witchcraft. Today it's called holistic medicine and sadly still not recognized by most in the conventional medical field as viable, which in my opinion is sad.
This is some additional food for thought on the subject...
You still hear the term "witchdoctor" used in certain circles regarding certain peoples and their beliefs. Now when you read the definitions of science below as per Dictionary.com: witchdoctoring, folk healing, and/or holistic medicine can all be classed as sciences due to their practice and the knowledge the practitioners garner through their workings. All three are forms of "systematized knowledge in general", but none are classed as a science the last I checked.
1. a branch of knowledge or study dealing with a body of facts or truths systematically arranged and showing the operation of general laws: the mathematical sciences.
2. systematic knowledge of the physical or material world gained through observation and experimentation.
3. any of the branches of natural or physical science.
4. systematized knowledge in general.
5. knowledge, as of facts or principles; knowledge gained by systematic study.