Pike and Musket Society
The Pike and Musket Society or the Routiers are a living history organisation whose focus is on the military aspects of 17th century Europe. It was formed in Australia but has international associations.
They concentrate on the Trained Bands (or "Trayned Bandes" if you prefer) of London during the period of the English Civil War. Even more specifically, the Second Captain's Company of the Green Band. The Society's aim is for as much historical accuracy as is practicable. Clothing, weapons and accoutrements are carefully reconstructed, based on historical research, preferably using primary (period) sources.
Their reasoning is "to take historical re-enactment seriously, and ourselves seriously not at all!" - the opposite tack to some other organisations.
The above description is based on the content of http://www.theroutiers.org/whatis.htm
The Routiers and the SCA
The Pike and Musket Society gives more importance to the historical accuracy of the construction and look of its props and actions than the SCA, but there are many areas of interest and discussions that have quite happily involved members of both societies. However, this mutual acceptance is not universal for all members. There is a historical habit of some members bad-mouthing the other society on the basis of previous incidents involving members some of which have since left the societies. Some of this ridiculing may still be found on various webpages.