"Nothing in life is to be feared. It is only to be understood." ~Marie Curie
The difference between holistic-style medicine and conventional-style medicine begins with a philosophy of how the world works. In German, this philosophy is called the "weltanschauung": your weltanschauung is your comprehensive view of the world and human life.
The predominant weltanschauung of our time is that our world is a machine, the whole universe acting as a clockwork with one part acting on another part in an essentially mechanistic and linear process. When a part breaks down, the way to fix the system is to find the bad part and remove it. Or, if it's a crucial component, replace it.
True to this weltenschauung, conventional modern-style medicine takes our bodies apart into various systems, functions, and parts, and focuses directly on those parts of our bodies that aren't working optimally. Disease is seen as a product of flawed equipment, and healing is therefore seen as equipment repair by biochemical or anatomical removal and replacement. To achieve this goal, conventional-style medical treatment usually involves the use of drugs, radiation, or surgery to excise the malfunctioning tissues so that the remainder of the organism can be considered "disease-free."
Holistic-style medicine, on the other hand, examines the entire body, the human that the body belongs to, its environment, and all the interrelations between these systems, as a single, whole being. That's because "holo" means "whole."
Obviously, to see and work with the whole system requires a completely different approach than the reductionist one used by conventional-style medicine. A holistic practitioner must use systems thinking, a complexity theory approach, and must know more about emergence, process, patterns, and other systems theory. A conventional practitioner, by contrast, must know a lot about anatomy and chemistry, since the conventional-style medical practitioner's role is to look for "bad parts" and replace them. Even if these parts are just chemical parts.