I think you need to understand that both branches represent efforts of humans to get the best out of the living organisms surrounding them. Food biotechnology is better known these days as genetic engineering, where scientists try to insert desirable genetic codes within organisms in an attempt to produce a desirable trait. Human beings have been trying to manipulate the genetic code for thousands of years, this isn't anything new. For example, the original corn plant we get the vegetable corn from is unrecognizable in what it produces compared to the ears of corn produced from corn plants today.
Similarly, herbal drug technology is a biologic application of learned medicinal qualities different varieties of plants are capable of producing. This aquisition of knowledge has taken place since antiquity; the application of this knowledge is nothing new.