An attunement is when one person opens another person and changes the electrical network of the person being attuned. Usually this involves attuning them to a different, sometimes higher, frequency of energy. The person being attuned must be open and allow for this to happen, and the person passing the attunement must already be attuned to the energy they are opening the other to. An attunement shifts this energy immediately and can be quite strong and felt physically. The affects can have dramatic results in the areas of physical detoxification, emotional letting go and spiritual awakening over a week or so. The results last for the rest of one's life.
An initiation brings forth what a person already has within them. After being initiated, the person is tapping into a resource that has existed all along, but maybe didn't realize. Most initiations are passed like an attunement, but not all. An initiation is most often a doorway that helps one to greater self-realization in a gentle way and over a longer period of time.
An empowerment is more like an initiation except the process can help you tune in to the qualities of the things you are being empowered for, i.e., an animal, flower or crystal/stone. The qualities of these "things" already exist inside of you and an empowerment makes those qualities stronger as well as giving you the path to them. Some are self-empowerments, opening yourself to them through intent alone, and some are passed like an attunement through intent.