Star Trek Enterprise takes place at an earlier date than The Next Generation.
what james said...although i must point out that mccoy crusher often turned to 'natural' remedies if they technologies failed them. mccoy grew up in the coutnry learned simple tricks there. crusher learned 'natural healing' from her grandmother.
Not more advanced (obviously) but Phlox's methods are vastly different. Phlox used what we would call 'natural' medicine, employing a great deal of cross-species work, such as using the enzymes of alien creatures to treat human diseases. His methods were most akin to the 'witch doctors' or 'native healers' who used plants and animals to effect cures. Like the Medicine Men, the methods worked because he studied the inter-relationships between species. McCoy and Crusher and Bashier and 'Zimmerman' used technological methods of cures.
