Reiki is an energy healing system. One learns how to channel (a type of funneling or calling upon) certain specific energies, and by "laying on of hands" (and other methods) one transfers the energies to another person who is in need of healing. That's an ultra-simplistic definition, of course.
Traditional Reiki is Reiki which has the seal of approval for whichever school it is which teaches the form of Reiki. Usually one is taught that there's only one right way to do it, and are discouraged from experimentation, or doing anything which might be considered radical. This helps maintain the fingerprint of the creator, and is generally a form of egotism on their part, to assume that their way is the "one right way" and to allow no deviation from the established "way" of doing something.
Non-Traditional practitioners are people who are bending the rules, constantly attempting to improve and learn more about their healing system, open to experimentation and input from others. They are going against the teachings of the popular schools of thought about Reiki in spite of the legal and cultural dangers of doing so. Non-traditional practitioners are being innovative with techniques, application, or are breaking new ground in the field of Reiki. Every new school of Reiki broke from tradition at first, to establish a new set of tenets or rules, and probably encountered resistance from the traditionalists who preceded them.
For instance, when the first person invented Karuna Reiki, and added it into the milieu in addition to Usui Reiki teachings, they were being nontraditional... they were teaching that there was NOT only one right way, that there COULD be more things added to the system, and that one could explore and innovate in the field of Reiki. Considering that Usui acknowledged that he only channeled a small portion of the available knowledge and use of Reiki, it would seem to be in alignment with the very principle of Usui Reiki that it can be further expanded upon.
Currently, Karuna and Usui Reiki are both normally taught in the "traditional" manner. Most practitioners you meet will be trained by traditional teachers, in traditional schools. This is not a bad thing, and we're not trying to tell people what to do or deliberately put it down; there is a lot to be said for traditions.
Non-Traditional teachings in the field of Reiki are usually highly frowned upon by the traditional schools and their followers.
Note that a number of the people contributing to this project are Otherkin, and that the project was originally called the Otherkin Reiki project: Otherkin are people who for one reason or another believe that they are not human &/or not from this world. Yeah, this includes aliens, but generally we're talking about people who think they are, or were in another life, a mythological being (i.e.: dragon, elf, djinn, mermaid, unicorn or whatever). For more resources regarding Otherkin, please see http://www.otherkin.net/
Open Source Reiki is the particular brand of non-traditional reiki being taught amongst the Otherkin community at this time. A bunch of people who are very sensitive to various kinds of energies have stumbled upon the teachings of Usui and Karuna Reiki, learned them, and discovered that they can make their own rules and applications for what already exists, and also expand on it.
Currently the "teachings" of Open Source Reiki are pretty new, and are given out with very little screening to persons in the Otherkin Community, because, frankly, for a lot of them, energy work is a "been there, done that, just couldn't figure out how to get it to work HERE". Some healers in the community have had little success with getting their healing techniques to work in this world... so now, they practice Reiki. Some, whether healers or otherwise, have a knack for seeing new symbols, so some people channel new Reiki symbols to fill the gaps in the current Reiki modality. In spite of advances in channeling symbols, there are STILL plenty of symbols out there waiting to be discovered.
There are several stashes of current Open Source Reiki knowledge. The references page includes links to most of them. The majority of the knowledge will probably be found on this website.
Notice: All information on these pages is intended as complimentary medicine, and should not be used as sole treatment for any illnesses. In all cases of illness, one should use one's best judgment to determine appropriate medical attention, whether physical, psychological, spiritual or emotional. These methods can be quite effective with the use of medical treatment and alternative therapies, there are, as yet, no known harmful interactions. As with all treatment programs, the use of Reiki as a treatment option should be regarded with conscientious research and approached with full consent.