I get asked this question a lot, as I refer to myself as a Wholistic Chef. Most people think that I just can't spell! However, it isn't a typo, there is a difference between the two words even though they are essentially quite similar!
Holism is a term coined by philosopher Jan Smuts. His definition was that "the whole is greater than the sum of its parts". Meaning it's best to focus on the overall picture as opposed to the individual details. It's usually applied to a much broader spectrum of themes and ideas, from philosophy to ecology.
Wholism sees the body, mind and soul (life force energy such as Chi in Chinese medicine, or Prana in Ayurveda) as the whole, and nutrition as one of it's parts. Instead of treating each organ as a separate entity, this view of nutrition sees the body as a fully integrated system. Understanding that there's usually more to illness than treating individual symptoms.
T. Colin Campbell, PhD explains this in greater detail in his book Whole: Rethinking the Science of Nutrition.
When I discovered I had problems with my liver, I realised all the different effects it had on the rest of my body. My hormones were completely unbalanced, I was feeling depressed, weak, achy, tired, and angry (and I was only 22 years old!). Once I understood how to heal myself through plant based nutrition, regular exercise, and meditation, I started to feel progressively better. I noticed the dramatic difference between how I felt after eating foods which were fresh and minimally processed (more life force energy), than foods which were heavily processed and essentially dead energetically. The minimally processed whole-foods helped heal the cells in my body, gave me more energy, and made me feel happy again. As an added bonus, it was nice to know that my food choices were having a less harmful impact on the environment.
Wholistic cooking looks at the bigger picture. It's about zooming out and consciously understanding that everything is connected: from the cells in our bodies to the ingredients we choose to fuel them with.