Mainstream healing means going to your doc, telling her what's ailing you, and getting meds, tests, or procedures - all invasive, physically, biochemically and emotionally.
At present, our understanding of the healing process is shifting because our grasp of consciousness is deepening. So many people already resort to alternative therapies, either to compliment conventional treatment, because they are at the end of the rope and conventional treatment hasn't helped, or even exclusively because it's gentle, without side effects, non-invasive, and relatively inexpensive.
If spiritual is simply defined as nonphysical or of the mind, then spiritual healing is healing without physical implements or methods, only using the mind or consciousness. Hence acupuncture, homeopathy or healing with essential oils, while acting on the body's energetic system, would not be considered spiritual healing, while prayer or healing through intention would be. Here is a website with a very helpful attempt at sorting out the different energy healing modalities.
Last fall I had the opportunity to do some writing and coordination work for Dena Barnett for her upcoming documentary Spiritual Healing: A New Frontier, a film that explores this vast field, which is still as yet little understood scientifically within our contemporary context, although it is the oldest healing modality. Spiritual healing, just like all the other energy healing modalities, can potentiate the healing process initiated by conventional medicine, it can also stand on its own as a treatment method. And sometimes it is more effective than conventional medicine in the many instances when Western medicine is unable to help. The UK is on the forefront of accepting spiritual healing as a proper therapy, and it is available upon request and covered through their national healthcare system. Exciting times ahead!