Being an online RPG, Riftforge also features organizations that could be described as warrior societies. In modern terms, Riftforge’s orders are more like a political/trade/religious organization with its own paramilitary wing.
According to Wikipedia, military orders are formed by religious organizations and this of course is correct in the narrow sense of “order”. However, how would you describe the British East India Company or its Dutch equivalent, VOC. They are both trade organizations that fielded a private army in the tens of thousands.
Finally, the third type of organization with a military wing is political. Numerous examples, especially in 20th century history.